A New Power Factor Bridge and its Application to Synchronous Machine Testing Citation Beckwith, Sterling (1933) A New Power Factor Bridge and its Application to Synchronous Machine Testing. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/pbcz-zg06. https://resolver.caltech.edu/CaltechTHESIS:10212024-203816811 Abstract No abstract. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Electrical Engineering) Degree Grantor: California Institute of Technology Division: Engineering and Applied Science Major Option: Electrical Engineering Thesis Availability: Public (worldwide access) Research Advisor(s): Unknown, Unknown Thesis Committee: Unknown, Unknown Defense Date: 1 January 1933 Record Number: CaltechTHESIS:10212024-203816811 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:10212024-203816811 DOI: 10.7907/pbcz-zg06 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 16805 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 22 Oct 2024 20:41 Last Modified: 22 Oct 2024 21:00 Thesis Files PDF - Final Version See Usage Policy. 14MB Repository Staff Only: item control page

A NEW POWER FACTOR BRIDGE AND ITS APPLICATION TO SYNCHRONOUS MACHINE TESTING Thesis by Sterling Beckwith, A.B. Stanford Univ.; M.S., Univ. of Pittsburgh In Partial Fulfil l ment of the Requirements for the Degree of Doctor of Philosophy, California Institute of Technology Pasadena, California 1933 OUTLINE Page I. INTRODUCTION .............................. 4 II. PO\V~ R F ACTOR BRIDGE CIRCUITS •.•.. , . . . . . . . . . 6 A. "Two-a.rm" Bridges . . . . . . . . . . • • . . . . . . . . . . 6 1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 a Accuracy of Phase Relation .... . .... 6 b Use Bf Capacitance . . . . . . . . . • . . . . . . . 6 c Use of Inductance •.............•... 7 d Stray Magnetic .Field Effects ....... 9 e Errors in Condense rs . . . . . . • . . • . . . . . 12 e (1) Dielectric Loss . . . . . . . . . . . . . . . . 12 (2) Stray electrostatic field effects 12 (3) Leakage effects .•.......•....... 12 2 Consideration of Final Circuit ....•... 13 a Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 b Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3 Balancin g of "Two-arm" Bridge . . . . . . . . ~ 17 B. "Three-arm" Bridges ........•.•..•...... 18 III.APPLICATIONS TO SYNCHRONOUS MACHillfES •...•• 19 A. General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 B. Accuracy and Range . . . . . . . . • . . . . . . . . . . . . 20 C. Effect of Tun ing in Galv a nometer Circuit 21 D. Test Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 IV. AJ\II:PL I FIER • • • • • • • • • • • • • • . • • • • • . • • • • • • . • • • • . 23 A. B. C. D. E. F. G. V. Chara,cteristics Necessary ............•. 23 Effects of Stray Fields . . . . . . . . . . . . . . . • 25 Vibration Galv a no meter vs. DC Galvanometer 26 Voltage Supply ·••••••••••••••••••••••• 27 Amplification Control ..........••...... 27 Galvanometer Construction . . . . . . . . . . . . . . 29 Ampl ification . . . . . . . . . . . . . . . . . . . . . . . . . . 30 SUMMARY AND COHCLUSIOHS . . . . . . . . . • . . . . . . . . . 3 APPENDIX. Calculation of phase defects of •.•.. non-inductive resistors ........••... 40 -3- SUMMARY AND CONCLUSIONS A new power factor bridge intended for measuring the power factor, and thereby the losses, of synchronous machines operating as synchronous condensers is described. "Two-arm" and "three-arm" bridges of all types are considered in detail and some types, incl~ding those previously used for synchronous machine testing, are shown to be inaccurate. The development of a tuned circuit amplifier for a galvanometer is described. Tests were made on three synchronous machines. Tests of one machine with high load loss indicated that short-circuit or "load loss" decreased rapidly with increase in terminal voltage. This decrease is substantiated by tests similar to the present AIEE test for l oad loss, but made with enough external resistance to produce a small terminal voltage. Conclusions are: the accuracy of the bridge method is limited by the stabilit y of the synchronous machine being tested; accuracy greater than that of the present methods of test can, however, be obtained; and me ~ surement of load loss under short-circuit conditions, as is now standard practice, gives a loss greater than the actual loss. -4- I NTRODUCTION Loss tests on synchronous machines have long been made by belting a small d rivin g motor or "tool 11 to the machine to be tested, a n d operating the machine at o p en circuit and then at s h ort-circuit. The loss a t full volta ge and full current is then assumed to be the sum of the 01Jen and s h ort-circuit losses. This proc edure is ob jecti onable: fir s t, because of the trou b le of be lt ing a tool and bec ause of be l t and bearing loss the tool introduces; and second, because of the assumption that short-circuit losses exist at full load. Both of these objections are overcome by the test method of this thesis, since the measurement of power factor and KVA requires no belt and since the measurement of losses under synchronous condenser conditions is certainly more accurate than measurement under short-circuit conditions -- at least for synchronous condensers. The presentation in this thesis deals largely with the subject of power factor bridge circuits and precautions necessary and corrections to be made in using them them, and with the subject of tuned amplifiers to be used with galvanometers. -5- The subject of synchronous machine losses as measured by the method described is not pursued in detaiil, as it was n·ot practical · to make complete . tests on large machines where load loss wa s appreciable. The one machine with large lo~d loss that was tested w~s an induction motor operated as a synchronous machine. The results indicated that considerable change· in load loss can be expected in any machine at other than short-circuit conditions. POWER F.ACTOR BRIDGE CIRCUITS ((for high voltage high current measurements) The bridge circuits used, or considered for use, in this study were of two simple types. which will be identified as "two- arm" and "three-arm" power factor bridges. Due to the few number of "arms", one is able to list most of the possible circuits and then select the most suitable one. "Two-arm~• Brid_ge~ In "two-arm"bridges, the voltage and current vectors from which the two bridge arms are built up are shown in Fig. 1. As _ there are only two arms, the problem (llsvalf'j } 0 (80°fo f>f/ is to obtain two parallel I voltage vectors whose rotations from the above vectors are accurately Fig. 1. known. In order to obtain a voltage vector from the given current vector, recourse must be had to a resistance drop or to an inductive drop, since capa-citance of sufficient magnitude to carry high currents at commercial frequencies is entirely impractical. Thus the current can be made to produce a voltage vector in phase with the current, ninety degrees ahead of the current, or at any other desired angle in the quadrant preceding the current, as shown by the conventional circle diagram. The phase relation be tween the current and the voltage vector obtained from it must be known to as small an angle of error as the angle of error allowable in the measurement of the power factor. If a power factor of 2%, for example, is to be known with an accuracy of½%, the maximum allowable angle of error will be .005 xcos -1 .o 2 :: .005 x 1 9 t =. .345 minutes (=21 seconds of arc): .005? degrees. If 0 the voltage vector is to be rotated 85° from the current producing it, to continue the example, the angle must be 85"±less than .0057 degrees, if 85"-±. less than .0077% or 85"±. less than one part in 14, 000. In a three phase circuit, this error of one part in 14,000 could be produced by a coefficient of coupling of l'1,oo~/n - one part in 8,000 between in- ductive shunts in the three phases. To obtain such low coupling between the phases with unshielded air core inductive shunts is not impossible, but is certainly quite difficult. If shielding were introduced, the losses in the s h i e l d ing iron would be so in i efinite -8- and variable that it would be almost impossible to determine the angle they introduced into the inductance. Consequently, although used in the first part of this investigation, air core inductive shunts and mutual inductance have been discarded as means of obtaining a voltage vector rotated from the current vector. There remains the one p o ssibility of using an iron core inductance, or a current transformer. Both of these involve not only calibration of error by labo~atory tests, since iron losses cannot be accurately calculated, but also the asstunption that magnetization of the iron and aging of the iron would not alter the calibration. To confirm the impracticability of this, the following quotation is made from a letter by A.S. McAllister, Acting Director of the Bureau of Standards. " .... inquiry concerning measurement of phase angle of current transformers to an accuracy of 5 seconds of arc." ( .08 minutes or one part in 32,000 of an angle of 85~ "This accuracy is well be yond that which is commonly attained in testing work and we are inclined to doubt whether you will be able to find a transformer which will consistently repeat its phase angle to this precision for any long continued period." Thus, at least with polyphase circuits, the only -9- practical way to obtain a voltage vector with an accurately known relation to the current vector, is by use of a non-inductive shunt. This point has been gone into thoroughly because it was the reason for changing from the circuit originally used to the final circuit. Also the values of one part in 14,000 de- veloped for maximum allowable phase angle error apply to any method of rotating the voltage vector as well as to any method of rotating the current vector, for which reason they will be used again. To c ontinue the discussion of "two-arm" bridges if the voltage of the "current" bridge arm is in phase with the current, the voltage of the "voltage" bridge arm must be rotated from the voltage vector by an angle equal to the power factor angle, and this angle of rotation must be known with less than the error of about one part in 14,000 as determined above. If rotation is to be produced by inductance of any type, therefore, the stray field linking the inductance is of vital importance. To illustrate this importance of average stray fields, a simp le calculation will be made of the field concentration necessary in any air-core instrument to reduce stray field effects to less than one part in 14,000 when the ins tru.vnen t is used under average "test floor" conditions. -10- Assume as average test floor conditions, that the stray fiel d is that set up by a symmetrical three phase bus of considerable length carrying 500 amperes in each line. The field due to one bus at a distance "d" cm from that bus, ~ill be: H = (Z I~" db•rnesl /ines/cmj.sin d ,, SOD • <,,rt =- •'€J /· /, ,nes;cm u1t l The field at the sa.rne point due to the other busses will be, under the conditions of Fig. 2, approximately :1.,1soo J ➔ .81,bs where 11 €i(w-t .... -i;g:) .z J<SOO .cj(u.rt ... ~) _1 qna c/+.8bb:5 c. s" is the separation between busses. The total field will therefore be: I I s: : ' ', ',~ p ·:-~--------,,:==---• ,, /5 ' ] =/DO{_ jurtfdI "". d-t-.8bbSJ s = f00 €. J"'t[ d (d-t.81,bS) J-1 Fig. 2.. If .866s = 2 feet = 61cm and d = 20 feet = 610cm, H 1' And if ::. JOOE.).,;t[ b I Li-10((,10-H,I) rlJ lines /c.n? 100 I I 7. I 1· / · 1.. = b?/0 - /,7. J me un ::;toli me "' I must be less than one part in 14,000 of the total flux, the flux through the mutual inductance must be == z.09 lines / cm 1... IL/-. ooo h?- I The ampere turns needed in a coil one inch in radius -11- to obtain density at the center of 209 lines/cm 2 is given by • • • NJ::. 2.0-f "- 2.S'f ::- 850 A(Tlpere Turns . 2..1T This, with 500 lrmpsj,,?- means a copper cross section of 1.7 square inches. The proportions of such a cioil are shown in Fig. 3. Thus, if the stray field assumed above is to be negligible, any air core instrument or mutual inductance must be of entirely impractical size and proportions. to be resorted to, If shielding is the shielding will concentrate the stray fields outside and will allow the inside field to produce iron loss. Such a shield would be cumbersome and heavy, and the re s ult would be hard to calculate, as any tests would have to be made at a series of currents to evaluate saturation effects, It has been shown then, that the obtaining of a voltage vector displaced by a very accurately known angle from either the current or the voltage of the machine cannot be satisfactorily acc omplished by means of an air core self or mutual inductance without prohibitive s h ielding and calibration. The possibility of using an iron core inductance is eliminated by the same considerations that have already been taken up -12- in connection with the "current arm" of the bridge i.e. aging of the iron core. Thus the only remaining possibility is the use of capacitance to provide a rotated voltage. The con- sideration of possible defects in condensers will cover: first, dielectric loss (or power factor); second, stray electrostatic field effects; and third, leakage effects. Dielectric loss. Since condensers with ordinary dielectrics have power factors of the order of magnitude of½ to 1%, and since the desired error is .0059 degrees, any ordinary condenser used would have to be very accurately tested to determine the value and constancy of its power factor. Mica condensers have lower loss than any others using liquid or solid dielectrics, but compared with the desired accuracy of .0059 degrees, even their power factor is high and wouli have to be calibrated. possibility is, The only remaining then, an air condenser. Stray electrostatic field effects. Since any condenser used could or would be shunted by a resistance of the order of magnitude of one megor.im, the stray electrostatic field effect would be entirely ne gligible compared with t he leaka ge effect. Le akage effect. With the condenser s hunted by approxi mately a me gohm, an d with a de s ire d error of le s s than one part in 14,000, the leaka ge resistance -13- between the un grounded side of the condenser and any source of out of phase potential must be 14.000 x one megohm ~ the ratio of the condenser voltage to the out of phase voltage X the sin of the a n gle between the two voltages == 140,000,000 for 10. 000: 1 voltage ratio. But the order of magnitude of the resistance of insulators is 1.000,000 to l,000,000,000 megoh~s per cm. cube. so that a square inch of dielectric only .01 inch thick would have 10,000 to 10,000,000 megohms resistance, which is more than necessary. Therefore the surface leakage is all that can be of importance, and as this is variable with dirt and moisture conditions. it cannot be calculated. However, by careful attention to this item, it can be made negligible. as it can be made to approach the resistance of any dielectric itself. If, then, air condensers can be made to provide sufficiently pure reactance without calibration or correction factor. they are the logical ones to use unless their inherently small capacitance makes such use pro hi bi ti ve. Consideration of Final Circuit There are many ways in which a II two- arm" bridge may be connected using air-condensers, that will provide wholly practical apparatus for the purpose, but we will confine our discussion simply to the circuit 4.sed. -14- in order that it may be quite fully considered. The circuit is s h own in Fig. 4. of which -PF is) Load ( to be meo.s~Yecl E I T• ftnu{ vacu • .., -t~be am pl,·(,,_,... 4nJ Col~. Fig. 4 load of which Pf ,s ) ( to 1,e mea ~ure,:/ [ I Circuit ori g inally used but d i s c a rde d due to stray field effects described on Page ID ]fig. 5 -15- (e f which PF is) Load lI9 };,e. mea.51,.,-e.q 'C~tihrr/le.c/ _ ..,__ Mw1"4/ lntlu.ciA11c.e __, ~ I Fig., 6 Circuit used by Churcher and Dannatt~ but shown in this thesis t o have important error due to stray field. (See Page /0). Accuracy As there are only two "arms" in the final bridge used, and as the detector was of the vacuum type, the consideration of residual errors at b alance is much simplified. -----·- ------·---------1. B.G. Churcher, "Alternating current bridge methods. Their B,pplication to electrical en g ineering problems with special reference to the testin g of synchronous condensers." Ele ctri cia.n I Vol. 101, pp518- 520, 545547 (1928). Also see B Hague, Sons, Lo n don. 11 AC Bridge lV~e thod.s. 11 Pitman and -16- The residual i n ductance of all the "non-inductive" resistors is one import a nt source of error. These residual inducta nces are c a lculate d in Appen d ix A, and are found to produce 50 cycle ratios of~ R of_b_ to,ooo 4 10,000 Since R is used in a 3 volt a ge divider, its phase error has no effect on the balance. The angular de- fects of R and R , however, 2 1 add and subtract directly from the power factor angle being measured, as shown in Fig. 7. Fortunately, therefore, they partly cancel each other. The only other error, besides those due to phase defects of the re1 _, R.,_ an Xe. sisters and the capacitor (which last is negligible), is that due to the condenser current, Ic, in Fig. 8, flowing :BL----'---- through the resistance, Ra, of the voltage, divider. As the drop -17- across R2 is fixed at about one volt by the sensitivity of the detector, Ic is fixed a t i amperes. Also the drop across Rb is fixed, as it is approximately equal to ::c fcXc:: Ic. ;:R.c=Ic.(cot0)RL a.ppr"'{.. ff -: :. 10 ro s-o Vrtppro ~ . Thus the tangent of the an gle o< of Fig. 8 is Le. fa.._ I1, T?b - r '- R.._ _ -i: · Ra.. _ 12 o.. s-o - below 10~ 0 so - , ~: ~ And if fan o< i.. will have to be soo • is to be kept Another way to eliminate error from this source is to make the volta ge divider of condensers or reactors rather than of resistors, so that the loading current Ic will produce an i~ phase volt a ge between A and C. Measurement of magnitude of resist a nces will be assumed to be readily accomplished with negligible errors. Balancing One unusual chara cteristic of II two- arm" bridges of the type described, is the peculiar procedure necessary for balancing. If, for ex~~ple, it is desired to make the drop E 2 of Fig. 9 ide n tical with the drop E1 , it is necessary to increase Eb and de cre a se E 2 alternately. But whereas, in the usual -18- bridge, v a rying of one voltage does not affect the balance of the other voltage , the varying of Eb wi ll change the balance of E 2 , and vice versa, so that the method adopted wa s that illustrated in Fig. 10, where the series of dotted "V- curves" are taken in order to determine the main "Vcurve. II The bottom of the main "V- curve" is the final b a lanc e point. '\"-' C ~ u ~ <l- ~ "- .., -I!!! I \ ~~ {-"' I I I\ I I -l-" /1 ~~ j<,-"' 'I \ I ' I / \/ \I 'I , 1' 11 () C " "' ,I {.,>.\ <.:) The bottoms Xe F,3- JO. of the dotted "V- curves" can be determined by eye or by plotting, depending on the desired accuracy. "Three- ~rm 11 Bridge~ All that has been said regarding II two-arm" bridges applies to balancin g. tt three-arm" bridges except t h e method of This is true becaus e the third arm is always small and at approx1mately a ri ght an gle with respect t o the other two arms, so that its presence does not appreciably alter the position or magnitude of the t wo main bridge arms, but only assists in balancing them. The easiest method of introducing the third arm in the particular bridge used, is to add a shunt resistor, since a volta ge in phase with the supply voltage is approximately at right a n gles with t h e current, and if the third arm is kept small enough, a ph ase defect in it of 10% is not prohibitive. -19- APPLICATIONS TO SYN"CHRONOUS MACHINES (of Power Factor Bridge) All synchronous machines are now tested under short circuit conditions and then under open circuit conditions, l.e. first with no current and second with no voltage, and the iron loss with full voltage and full current is assQmed to be the sum of the no-load iron loss plus the short circuit losses. A more simple and more accurate way of obtaining not only the iron losses , but all the "annature input" losses, (F & W, 2 LL, Core L, and Arm r R) is to measure the power factor when the machine is o perating as a synchronous condenser, that is, drawing full KVA but delivering no mechanical power. For synchronous condensers, this method of measuring losses gives exactly the desired loss, but for machines operating at other than zero power f a ctor, there is some slight difference between "condenser" losses and the desired loss, due to the shift of the axis of demagnetization with power factor. This effect of chan ge of loss with power factor will, however, be taken up later when short circuit losses are considered. Another advantage of the determining of armature losses by the determination of power factor is the ease of making the determination - no -20- belts or auxiliary driving motors being required. The only theoretical objection to the method is that any measurement that is made must be limited to fundamental frequency components of current and voltage, and that if the loss due to harmonic currents is to be taken into account, separate measurements of the power factors of the different harmonic currents and voltages will have to be made. The necessary accuracy is not gre a t, ~s the accuracy of the conventional method is not great. Eight per cent error in the total loss would not be prohibitive, and three per cent error would be very satisfactory, judging by the accuracy of the present methods. One factor that would ·hel :.o the accuracy considerably is the lack of belt loss and increase in bearing loss that goes with it. The range of power factors to be measured by the bridge method would be from a minimum of one per cent for a machine with one per cent armature loss, 7 up to a maximum of ten or fifteen per cent, at which point a wattmeter reading full scale with t Nenty per 1 cent power factor would be easier to use and sufficiently accurate if calibr~ted. The maximum accuracy was found to be limited by machine instability in all the tests made for this study. It was fir st thought that this instabilityy -21- was due to variation of line frequency and voltage, but after trying storage batteries as a power supply (thru a motor generator set), and for excitation, it was found that almost as much was accomplished by using storage batteries for field excitation as was acc omplished by using storage batteries for the entire power supply, and that even with a storage battery supply enough instability remained to limit accuracy of balance to about one per cent. Later it wa s found that a direct connected exciter was quite satisfactory. The displacement of the test points from the final curves is a good indication of the a.mount of instability that remained. Fig. l? shows a curve ta.ken with storage battery power supply and Jfig. 18 a curve taken with one motor generator set for excitation and one for power supply. As mentioned before, a tuned galvanometer circuit was use i in all tests so that only the fundamental of current and voltage was effective. The neglecting of the harmonics of voltage and current is due to the close approximation of the voltage and current waves to sine waves, as shown in ]'igs. 24 and 25. Even if one har- monic of both the current and voltage waves were 5%, and the harmonic power factor were 30%, the consequent loss would be only .05 x.05 x.30 =- .00075 of the machine K>IA, or about • 0 :~6 5 -= .00?5 =- ¾% of the machine KW. -22- This question of harmonics has, however, potential importance. as it would be valuable in design calculations to know which harmonics represent loss and ; 1'Vhi ch do not. Test Results The significant test results are shown in Figures 18, 19, and 23. Those figures which have not been dis- cussed are practically self explanatory. The align- ment of points indicates the accuracy of balance; the comparison of the tests with tests by the standard AIEE method indicates the expected agreement; and the consistency of phase differences in Fig. 18 indicates accuracy over the full range of voltages. Three different machines were tested: a standard lOKVA four pole GE laborator y a.J.ternator; a standard 15KVA six pole Westinghouse laboratory , alternator; and a lOHP eight pole Westinghouse wound rotor induction motor operated as a synchronous condenser. The first had 15% load loss , the second had 5% load loss, and the last had 40% load loss when used in this manner, which 40% load loss is the reason for the induction motorts having been tested. The points near the lower end of the curves of Fig. 23 were taken by the same method as the short circuit point, except that external drop was produced by a resistor, and its I 2 R loss v1as subtracted from the measured loss. -23- AMPLIFIER Calculation .Q.f. N:ecessary lletecto!: ffllaracteristics The Power Factor Bridge circuit is shown in Fig. 11. The type of detector needed will depend on the wave shape of the current and voltage, and on the accuracy of balance desired. For the purpose of the following calculations, 10% voltage and current harmonics and 1% accur9.cy of balance will be assumed. Also the voltage across R will be assumed to be one volt. 1 rbw-e r S'-<ppl:J Fig. 11 Then the third harmonic current through Rz: R +- ·x (fundamental current through R2 )x R2 ~L~X: 2 + J3 C (fundamental I ~( 1 + j 2 0 ) : R2 1 + j 6.? (fundamental of line current)x approximately 3. Therefore the t:hird harmonic across R 2 ~ approximately 3 x (% magnitude of harmonic) x fundamental= 3 x ( • l) x ( fundarn.en tal) = . 3 x:· fundamental •. -24-- lifext, the third harmonic across ,: R1 =.l x fundamental, since 10% current harmonic is assumed .. But, referring to the voltage triangle OCD of Fig. 12, E it is seen that the power factor is the ratio of CD to OC, and if the power factor is to be measured to rL l?l within 1%. the length CE _:must 1 G.nc( r ... R~ C be known to within 1%. If D I - - - - - - - - ___ .Jo OC (:voltage across R1 ):l volt, then the voltage to be measured by the detector at balance is .Olx CD: .01 x power factor xOC, = .01 x .05 x 1 volt : .0005 vol ts : .0005 x fundamental. Therefore the maximum ratio of the third harmonic to measurable fundamental will be • l -t- • 3 • 4 = 800 .• 1 .0005 1:1 .0005 For .01 power factor and .001 accuracy, the th i rd ratio = fundamental = .00001 • 4 = 40 ' 000 •• 1 And if the third harmonic must be less than 1 5 of the fundamental in order to cause no interference and to give a sharp balance, these ratios become 4,000: 1 and 200,000: 1. For .01 accuracy and .65 power factor the minimum fundamental to be detected: power factor x accuracy x voltage across R1 = .05 x .01 x 1 : . 5 MV -25- For .002 accuracy and .02 power factor, the minlimum fundamental to be detected = . 01 x .001 x 1 = 10 microvolts: .04 MV. Consideration of Ef f ects .Qi §tr.!U" Fields Due to the ordinary stray fields present on a test floor, it was found that air core inductances were entirely unsatisfactory, even after the last step of amplification. As an example, a 100 henry air core inductance with approximately three pounds of #36 wire and a diameter of twelve inches was found to pick up a volta ge of ten millivolts when four feet from a small lOKVA laboratory alternator. It was also found that almost any iron core inductance was affected too greatly by stray fields to be acceptable. The only exception was a coil (Western Electric 25A Repeater Coil) which apparently had no air gap or non-overlapping joints in the magnetic circuit. This coil could be used before amplification if properly shielded by an auxiliary heavy sheet metal case. The absence of inductance coils in the final circuit was due to the desire to eliminate with certainty the effects of stray fields. -26- Vibration Galvanometer ll• DC Galvanometer One disadvantage of the condenser a.nd resistance tuning was that the detector was more sensitive to frequencies below fundamental than to fundamental, but Fig. 13 enough sub-synchronous voltage hannonic was found to exist in all machines tested to cause some trouble. This hannonic is shown in the oscillogram 2 of Fig. 13, and its effect is shown in Fig. 14, where the narrow V-curve was -08 taken with a vibration galvaFig. 14 nometer relatively insensitive to low frequencies, and the rounded V-curve was taken with the DC galvanometer with rectifiers, which instrument was more sensitive to sub-synchronous hannonics than to fundwnental. 2. This oscillogram was taken with the original bridge circuit shown in Fig. 5, but the effect would be identical with the final bridge circuit. -27- Voltage §.u12ply The use of rectified AC for the plate supply was not possible, as the amplifi.er was tuned to be most sensitive to low frequencies, and it was necessary to obtain zero output with zero input. The use of AC for the fila~ents, which were of the heater t J~e, was tried but found to introduce line frequency into the output. The use of rectified AC for the filaments was not tried, because a storage battery was easier to obtaini However, even rectified AC would introduce so~e coupling with the AC source, and consequently much greater care would have to be exercised in grounding the amplifier to the machine being tested. Because of the critical nature of the screen grid tube, it was found that a separate plate voltage source was essential for the tube preceding it in order to prevent "motor-boating." Amplificati9n Control Due to the fact that the fundamental components of the two voltage arms of the bridge were opposed to each other, leaving very little fundamental but almost all the harmonics to impress on the amplifier, the voltage in:pu t to the amplifier appeared very much as in Fig. 15. It wa s e s s~ntial that the input be -28- connected directly to a grid, as any current drawn would unduly distort the bridge circuit used. If, however, the first tube produced much Fig. 15 amplification, it might amplify the hannonic voltages so much as to block the g rid of the next tube and reduce its sensitivity to the fundamental voltage. The scheme followed was therefore to use a three element tube, with an ampl ifi cation constant of only five or six, in the first step, followed by enough tuning to prevent blocking·of the next grid by the harmonics. As it was desirable that the sensitivity of the amplifier be extremely variable, in order that it could be progressively increased as the balancing of the bridge progressed, the output of the first tube was fed into a potentiometer, which gave variation from zero to maximum sensitivity. This arrangement was very satisfactory and was found to be very convenient to use. The necessity for some such device is due to the fact that the ordinary expedient used in balancing bridge circuits, i.e. observing the direction of deflection of the galvanometer needle to determine which side of balance the bridge is on, could not be used with either the vibration galvanometer or the DC galvanometer with rectifying circuit. -29- Galvanometer Construction The AC vibration galvanometer use~ was originally built, for reasons of economy, from the magnet of a standard GE oscillograph vibra tor. It was later found, however, that the magL1etic circuit of a commercial vibration galvanometer was so sensitive to stray fields that it was necess a ry to provide considerable extra shi e l d in e to o btain a zero re a ding whenever the instrument was within several feet of a small lOKVA laboratory alternator. The oscillograph ma gnet, however, wa s suffic i ently compact an d of such a material that it was not influenced b y the same fi e lds that af f ecte d t h e comn1ercial instrument. The recti f ier used with the DC galvanometer was one of the standard instrument t ype of full wave copper oxide rectifier. It was supplied by West i n ghouse. The resistance curve for this type of rectifier is shown in Fig. 16, as such infonnation was almost essential in properly matchin g the output of the amplifier. Curves are also shown for a crystal detector using a galena cry stal and one or five catwh iskers. An attempt was made to ct ange the characteristics of the copper oxide rectifier.when operated at about one micro-ampere by reducing the area of contact between adjacent oxide -30- and copper surface, but no appreciable change could be effected. Amplification. The calculations ma~e under the heading "Calculatio n s of Necessary Detector Characteristics" showed that the minimum input vol ta.ge to the detector might be as low as 40 micrOvol ts. From the curve of Fig. 16, it is seen that the necessary output voltage with a DC galvanometer re quiring one micro-ampere is .04 vol ts. Therefore the amplification in the detector must be .eooozr or 10,000. .04 A PPROXJMATE" 1?[515 TANCE q ~-=------,---,--~--..:;._--,........,~:--::~=-'""'i•;....__-;----,---,-,----,t c:Jt:ua 1----l----1----l----+--- ----1----- ~!°/\ -!----il--1---+-- --+-- .., - + - - t - - + ---+-- --------1 ~ ~ L----l.-l--l---1-----I---H-l--+---t---Hr-t---r--i1! ,- 1 ----l----1----l-- - - + - - -----l----- -1--1-----l---+--- - + - - - + - t - - t - - - - + - ------1 ~ ~ :---:> ~ /npu1 ¼ f,._J/ Wave t•ppt-r Ot:i"t:Je )::,._ ~ ...__ - 4 ~ --- ---1~ ~ {f /'-IF /'ff HbV .i..,- . 1:, :iJ MF.. :MF .ooc 7- 1 T""I- - - - ' - - - ~ - - fo ;, ..n Vrb,-, Ga I,,) AC Ou.fp,,,_f (t, 1. 1"0.ri. vc Gttlv) DC Ouipuf {?ec,t;f;er - [nslrum~t ; { Tijfe ---J --- c::::: 3'i \) -==rj ·1·::- :i ~ <') ~f !J .A ="Iv~ .. 2. 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L ~ '.t: !:1:1 l .)..; ~ ,,.;..i :!:t ·t- -1 4 ;:n ~a 1-+ I 4 ~ rt l :t.,~t ~i= w.. '.Ii '-\l b. ~ ·" Ero R§. ~ o:'i ~~ -~~ -- :r.. t ! + ::: +tT ~ , , ~ ,- $H .,.. - -. • ij ' t -,· t- t + +! - ~ l:t±Jttt±:tt:tti C --.._ ~ - 31- WAVL Wes Ti,, ty/1" L< se I ndu cTio n 4S 5'.l" CiPndtn5er- - - - - cl.(_ IOKf/A # /1 aTar tt I b o b II S CW 1? .. nrittj C£ rORMS 1 rr tn /...a.b,,r-ati,-'j A/iernafor- 52b8ozb t_,.,,_ rre 11 t ----.. APPENDIX Calculation of Residual Inductance of Non-Inductive Resistan c es I. ~d:.lal ,.J_11ductance 9.J R:i:-_Q:( Fig. ~ The dimensions of this resistor are shov\'n in - A formula for Fig. 26. the inductance of such a s haped coil could not be obtained, so that it was necessary to develop an expression from the formulas for the self and mu tual inductance between two parallel conductors of finite length. Fig. 26 The total inductance for several pairs of parallel wires carryinc; current in al te rna te directions is: L 0 - 10L1 -2M1-2 -2M1-4 - 2M1-6 -2M1-0 + 2Ml-3 + 2M J:-5 + 21VI1-? -2M 2-3 -2M25 + 21'13-5 • • " • • • • • I e ....... + •. • .•• -2M45 .... e.t"c... - 16L 1 -2M _ +4TJI 1 _ -6Ml-J.4 + 81VI 1 _ 13 ••. 15 1 16 • . • • + 2BM 1 _ 3 - 30M _ 2 1 -41- To calculate Land M, formulas 135 a nd 174 in the Bure au of Standards Circul a r 7 4, "Radio Instnunen ts and Standards," are used. Thus where dist an ces are in ce ntimete rs , L l. : and M ,002xl [ 2. 303 xlo glO b - .002 [ 2.303 -- lfrom these• L .i,; +. 5 + , 2235 (bac)] )' H 2 x i xl 0 g10 J~~-Vl-..-tD ... -tD] .1072 ; H Ml-12 - .090 Ml-3 = .0712 - 0 L\. - .0328 Ml-10 Ml-4 -- .0600 Ml-11 ::: ,0318 Ml-5 = .0530 M.1-12 = .0296 ;;; .04?6 - Ml-13 = .0276 .0430 Ml-14 -- .0394 Tvll -15 Jvll- 6 Ml-7 Ml-8 • Ml-9 Therefore Lr esidual : 7, ,. uO _ = . 02 58 -- .0242 - ,0228 Tull -16 - 7 .124 -6.933 = . 191 ,f H X _ . 191 x5O x21f xlo- 6 _ a nd • a t .50 c ye 1 es, 1? - .1 6 10,000 II . Re s idual I nductance of R2 of Fig. 4. This resistor was a wire-wound 1½ megohm resistor, of the dimensions s h own in Fig. 27. -42- □ QJ~J~,/q g g=G]•r<W-ns Turns pe.r u, i / = 4,1,,00 oppro l. Fig. 27 From f o r mu l a 158 of the U.S. Bureau of Stand a rds circular #74, . Lu -- •· th e s elf indu c t a nce of on e coil is: 660 , 000 _ft H : 2/3 henries An d fr om f ormula 188, M t h e mutual in duct a nce is D ) -- .0140 for coils 1-2 -- n~Fa where F = fn 3 ( Vo'-+'-\a.. ... 1-3 -- .007 for ') II = .004 " II 1-4 ..- .0021 II II 1-5 II II 1-6 II " 1-7 II " 1-8 = .0016 = . 0011 -- .0007 -43- But, as for the inductance of :B'ig. 26, the total inductance is: L - 8Lu -14M~ +12M1 _ 3 -lOM1 _ 4 48M1_ 5 -6Ml-6 -1,4111_7 -2Ml-8 ~ .66 x8-14 x.347+12 x.1?3-10 x.10+8 x.052-6x.04 +4 x.03-2 x.02 = 1. 8 henries Therefore at 50 cycles, ~ -rr x50 xl. 8 4 approx .. = 2 115 xl015 - = 10,000 III. Residual Reactance .21 B.;3_ .Qi :Fig._!. The reactance of this resistor was covered by formula #167 of the U.S. Bureau of Standards circular #?4, but since the formula was found to be incorrect, and as a bridge suitable for measuring the reactance was avail~ble, tests of the reactance were made. These tests showed reactance of about .4 millihenries one scale division on the bridge inductance being one mill ihenry. Consequently the 50 cycle ratio of~ R 2 1l'" x50 x. 4 1250 1 - 10,000 _44... r 42.. TIA.rf/5 /nc/1 0 f ?F J,S w,·r.e. 2." 1 1. '' x L" bQt ~ (,-1e 31. Dimensions of R3 of Fig. 4 Fig. 28