| i l I‘! L ‘I ll 'III M: I ‘1 “I! l I l r \ H l l W U \ WI § I ,1 ‘l \l i \ H U W 1 1", u i AN ARTIF1C!AL TRANSMISSION LINE ’Iixeasés {err irks. fisg‘me 9f M. S. MCCHEGAN $315.”??? COLLSGE ‘ ’5?er Ray ’“v’éncen? W68 ”IF—5‘5 '_ ,. H.796 Date This is to certify that the thesis entitled An Artificial Transmission Line presented by Wilbur Ray Vincent has been accepted towards fulfillment of the requirements for ___!°_§°___degree in_§2_E_L__ Wkfi/FA— UMajor professor June 10, 1948 AN ARTIFICIAL TRANSMISSION LINE By Wilbur Ray Yinpent A THESIS Submitted to the School of Graduate Studies of Michigan State College of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTLR OF SCILNCE Department of Electrical Engineering 1948 13-15515 Preface Transmission lines play an extremely important part in our everyday lives. Power and all types of communication over short and long distances are carried over transmission lines. A thorough means of studying the characteristics of transmission lines could be available in every Electrical Engineering Laboratory. It is the purpose of this paper to describe the design, calculations, and testing of a Lumped Artificial Transmission Line built by the author for use in the Electrical Engineering Laboratories of Michigan State College. The author is indebted to Professor B. K. Osborn for his many suggestions concerning the design of the line and to Mr. Robert Nelson for his suggestions and short cuts in the laborious mechanical construction of the artificial line. 2.1 2.2 2.8 2.4 2.5 4.1 4.2 4.5 Table of Contents Chapter I Description and History of Artificial Lines Chapter II Electrical Design Choice of the Circuit Derivations Calculation of Section Constants Error Introduced by Lumping The Lattice Network Chapter III Mechanical Design Chapter IV Tests and Results Voltage and Current Measurements Impedance Data and Curves Determination of Line Constants by Impedance Measurements Location of Faults Square Wave Testing Chapter V Conclusion References Bibliography page 3 14 17 20 22 30 46 60 68 CHAPTER I Description 2: Artificial Lines and Their History The principal purpose of an artificial line is to furnish an electrical model of a corresponding real transmission line. Thus the electrical behavior of the real line can be imitated by the model. The laboratory student can gain much valuable information concerning the behavior of transmission lines, especially in the behavior of long lines which are easily obtained in the artificial form but hard to study in their actual form. In general, artificial lines can be classified in two ways. 1. Smooth lines 2. Lumpy lines A smooth line is available in the Electrical Engineering laboratories at the present time for use of students. This line consists of parallel conduc— tors wound upon long insulating tubes. Smooth lines have the advantage of imitating, exactly, the electric conditions of real lines for all frequencies and transient conditions. They are apt to be very large in physical size and hard to construct especially in a long line. Also it is rather difficult to obtain measurements upon this type of line. A lumpy line is made by lumping together the values of capacitance, resistance, inductance, and conductance for several miles of a given line into a section. Lumpy lines are usually simpler to construct, more compact, more durable, and less expensive. It does not however, imitate the line for all frequencies and conditions. Measurements can easily be taken at several points along a lumpy line. The first artificial line’known to exist was constructed by C. F. Varley in 1862 for the study of submarine cables in England. This was a lumpy line consisting of alternate sections of resistance and capacitance. The first artificial line used in this country was built by M. I. Pupin in 1898 for use in the laboratories of Columbia University. This line consisted of distributed resistance, inductance, and capacitance. Many of the early lines are described in the literature along with the data obtained upon them. The basic ideas used in the early artificial lines have not changed and are very similar to the line this paper describes. I do hOpe however, that the many refinements in construction and in the ease of taking readings will make it more adaptable to the study of present day transmission line problems. CHAPTER II Electrical Design 2.1 Choice of Circuit When designing a lumped artificial line one has the immediate choice of several types of electrical structures. The line constants can be lumped together into a T section, ITsection, H section, Ilsection or a lattice network. The type of section used is determined largely by the cost of building and the degree of accuracy. I It was decided to approximate as nearly as pos- sible a pair of 104 mil wires spaced 12 inches. This is the usual Open wire line used in telephone work. A study of the materials at hand which were made available through government surplus and that which is listed in several manufacturers catalogues seemed to indicate that an H or balanced T section would allow us to build the best possible line in the most economical manner. This would allow us to use a block of high voltage precision mica condensers available in the surplus stock for the necessary capacitor. A standard size 5.3 mh. R.R. chokeeseemed the logical choice for the necessary inductance. Calculations shown later in the paper will show that the resistance of this coil is very close to that of ~3~ the equivalent lumped line. Thus, it was not neces- sary to purchase resistors for this purpose. Also by using the standard 5.3 mh. R.F. choke the use Of an inductor with an iron core was avoided. This means a line which more closely approximates the Open wire original over a wider band Of frequencies and one upon which transcients can be observed along with the possibility of using a carrier type transmission above the audio range Of frequencies. Measurement at the end of each section can easily be provided by a system Of normaled Jacks which are also available in the surplus stock. The Operation of the Jack system is evident from the circuit diagram which follows. By using the H section as a unit, half sections which are inserted into the usual lumped line for measurement are eliminated. This makes the measure- ment Of voltage and current a simple matter of plugging into the Jacks at the end of the desired section. Up to now I have inferred that the values used in a section of lumped line would be the sum of a certain number of miles Of equivalent Open wire. This seems to be a very logical answer, but are the Characteristic Impedance and PrOpagation Constant of the lumped section equal to that Of the distributed line? The following derivations will show that for our purposes they are -4- 6 the same and will point out the small error introduced by lumping the line constants into an H section. 2.2 Derivations For convenience in the following derivations, the H section will be reduced to an equivalent T section. ji_ S‘ ' a 2; Z, I: ”23 o————] }—UL—['1——o e——— ~———o a a x. z. I 20) : Z’fzj' Z 202’ = Eu Z3 - 2.2, .. zamzfliix 3. ZS] " Z; f szé - 21,25 2&7 _ letfztzsitzlg} . Z 2 ~——’-—— - y :1 29* 3’23 21/23 Rearranging l and 2 and substituting into 5 55 :,Z@ "Z3 Z; : 502. -2? 23/::inZQ-ngEanéS’LEE‘Vquib'iétyzzzgl'zht 20.2 .2 ZS] 24.3 3 24/ 202, " 2:; (5: 23 ‘3 )ffgaz (24"2357 5: 25‘: Ziv"J/§;z {331351) Z 2:21,:Zdl' yZu, (Zn/’ZSIS— Let us leave the lumped section at this point and find the values on 20,) 3.2,) is", 4”0/ 2.9.2 distributed line. for a Considering a small portion at? of a long transmission line J7 Y 0’]:- -vr Ji 7. JV: 4sz /0. ”If- -VT ow // 0/]: ~18 /Z. 0:? 9/! /3. (KL—V- —3 c” “7.- Substitute 10 and 11 in 12 and 13 .2 ,7 J )2?!” :7 :27 Y” Which is a standard differential equation with the solution of the form ; - M .2”: Ar (+53: M y: xii/1+ 6; 6"“ I! Solving for the constants Of integration A1, B1, A2,132, -c} if: M,6’M,~rfic’J i; M a”- my H ~vy me ”.48 a H -Ig —.— MzeHWE’z 6‘“ Considering the boundry conditions at the sending end Of the line where 130, Vllé M 111-5 ZS: A,f,8/ K, = 4&6}, ~Ky= rA,~d'BI ~T,Z= M245; Solving the four equations for A1, B1, A2 and 82 ’ A/sz(J—J'Ks}f): (XE-Kg) .530 «\x (\ SN -+ 5 2‘5 I! Nl‘ N\\ N\\ (\‘\\ C4) * CK s \__z 32, 3%,(L/gf’rsgo) Substitute in 14 and 15 -fi{ agatflééé «fig—fa” -u - Vzé’l/S 6H—EA,73246 félégdrl-ffjszoé’ 11,71,235" 11 -9... Where I is measured from the sending and of the line, (zygy aw? g,:y_§g1 \ A similar pair of equations could be deveIOped by considering the boundry conditions at the receiving end Of the line. IX. f:f,,M/Jf§fwfl 1?. V= AM“ + a;,,MH It might be well to sidetrack here for a moment tO get a better picture of the quantity.Zb. Taking equation 1'? and dividing by MM and letting [—4700 V xdkk/f/ 37M ”/5 “J3 3" Mr! 0 '3 Vs ’L 20 V Z Z.=-i:/: 2: yr 2213 the impedance Of an infinitely long line and is called the Characteristic impedance. Now to return to the original aim of determining 27o, and %,Of a distributed line. Considering equations 18 and 19 for the Open circuit case with. IL<=0 V4, , 1—:‘§:,JLM/Ib( 1/: ,4, MHM - f/ 3“ 5‘ 3017M .[ 20 MM 20¢ -10- Considering the short circuit case with equations 18 and 19 where V/LZO [:12 Mi/ szflgéxQJ/U’ ,L/~ 4AM 38¢3I'20Mr1 ‘22:,=?2?o;fzaA/It/ Substituting the values for 20 and 21 into equations 5, 6, and 7 23 3 [27021301 ‘2!) : VZAZMMMTBJHJ 2‘.ng: ‘/fl%'%flfi I ”Q. \ \d -11- Z/ t 20 fwd 5—H eff-”5"“ [J2me]; 61+é’ mail J J :3st {If 23. Z/:%:Zo+W/zg Thus the equivalent T section for a length,X Of distributed line is 23072.15! 2.131% If’ééis.small we can use the following approxi- mations (9P9 Hp e'flgl-J Mi m1; :1: —12.. ,» / 7 ”F2712 20.” 23:: 3%,: And the series and shunt elements are merely those which would be Obtained by lumping the distri« buted elements of impedance and admittance. ~13— 2.3 Calculation of Section Constants The line constants for a pair of 104 mil wires spaced 12 inches are as follows: R =10.15 ohm per loop mile L h .0036? henries per mile C .00835 micro farad per mile G: .80 micro 3%: per mile For reasons described earlier in this paper the inductor used was a 5.3 mh. choke coil with a resis- tance Of 14 ohm per coil. The following calculations in determining the lumped constants for the H section then became evident. .53 w: as M'J/W Big/”Veg" : dj/fM/fljm 3.657”W{Auf a: 0:77X,&Ji3d’= .ayizxif/fl/fi; fi7:/%§/Xai7/ = éVt/mvzawzg [3 £241 : Afil/Jb/M 7/ 1. %/.21/f( Mg/fllofi’ 6 g , fir/{11577; K? - .41 : _,j2:£— : él/é;/J&-Jz>/;aziée R - c5 ¢Zgfil -14~ Several hundred dollars could be saved by using existing materials and for that reason the values actually used in the artificial line are slightly different from those calculated. The difference is very small however and the error introduced is also very small. The values used are listed. R3 14 ohm per coil 5.3 mh per coil .048 micro farad per section leakage Of the insulation used in construction -15.. mums 23.3 a 8.22 a... a at: 9 IMHPIIM: E E E than QII and: «Shun. J: W WW . dim: stash...“ 2.4 Error Introduced by Lumping It is often important to know the limits of accuracy Of a lumped line. That is how far are 20 and )1 from that of the equivalent smooth line. For the lumped H section line we have derived: 24. 2, = flamm) 27. 22::£(6¢ch) For a'T section we have ,2 . 0/: , t z] 2; 2? 2?2? :/§73? l)f.722 For the smooth line ’27 Z ENAM- 6¢ch Substitute 26 and 27 in 28 ’zyt?mué ‘* "357255 ///f C—J—W J” J JG) 9’ :20 /f{%£)2. We see that 20 differs from Zlby the factor 1/7%(§‘—f,)2 This radical is easily eXpanded by the binomial therom which gives us 2%: Z.[/+Z ”W MW hi)” 2‘""] Simplified and neglecting higher order terms Z’.(/+ Ci) Where 51 y/ (if. f c 3,4 (%)2(£+JwL)(gwwq Since the error is largest at high frequencies where R is of little effect and G usually negligible we can write ”- 351$ " LVN—gs); Which to a very close approximation is the difference between EQIand 2% . Repeating the same line Of attact we can find the error in the prOpogation constant introduced by lumping the line constants. For the smooth line the prOpogation was eXpressed 88 30. M: #37 =J ([zuwmgm For a series of lumped )1 sections 3/. J”? =01M'7gg Substitute and in J31]: £hM~l 92%;" Expanding the series for ”ilk/"ii/ w waaffawnfi-n] 3 b” Hg?) -18- The error Jet (3W Examination of the two errors shows us that The error in¢{1—is of the Opposite sign and three times as large as in.[% . For a given 22the error increases with frequency hence should be calculated for the highest frequency at which the line will be used. For a given frequency it increases as the square of the length and decreases as the reciprocal of the square of the number Of cascaded sections. The calculated error in this transmission line at 5000 cycles per second is a 3 .de “2 (1)2 : ~. g r 5 3 3 .2 - 3,67X/a’314fi351w"€737,1/19au/o‘ (2.3.7 - m 7 ,l y . ,/CZA' ;Z/544JU “~Zgo" 6(79 .a/77/3 1/00 2,5 The Lattice Network The Lattice or Bridge type structureéis the most general type of electrical network. Its design equa- tions are simple and easy to handle. The character- istic impedance and prOpogation constant are derived from the following diagram and considerations which are used earlier in this paper. From the above equations we see that the Characteristic Impedance or the Propogation Constant can be varied without changing the other. This is not possible in either the T or}! structure and is a decided advantage when designing general structures. Also networks can be formed which do not have an p-20- equivalent 7'OrZT structure. This will be evident upon inspecting the following conversion of a 7'to a lattice network which is based upon the fact that the Open and short circuit impedances must be equal. From the above equivalence, the prOper values for the elements to be used in an equivalent section Of artificial line can be calculated as follows. {EN PM 3 + be at” in ll % it (a 8' ?\ u / Ma c = ,Mowf _ ~21? CHAPTER III Mechanical Design Rack and panel type of construction was decided as being the most desirable from many standpoints. A standard 7' steel cabinet was available through govern- ment surplus which made a very neat appearing and convenient container for the artificial line. Aluminum panels were used to facilitate accurate drilling of the panels for the mounting Of the Jacks. Mounting and shielding panels are made of No. 16 sheet iron painted black. The panel designs are shown in the following drawings and the assembled panels are shown in the accompanying photographs. The panels are designed so that complete shielding is Obtained between each section. The placement Of parts in the H section are shown in the panel assembly photograph. The photograph also shows the mica condensor assembly each Of which is made up Of six separate condensors mounted together with threaded brass rod. The total condensor assembly being mounted on a bakelite strip. -22.- 1 ea. 10 ea. ea. ea. Parts List Standard 7' Relay Rack Cabinet’ 7" x 1/8" Standard Relay Rack Panels-Aluminum 3" x 1/8" Standard Relay Rack Panels-Aluminum 3' x 8' NO. 16 Sheet Iron 3' Lengths of 1/8“ Brass Rod gross 8-32 Brass Nuts gross 6-32xé Brass Machine Screws 2 2 8 2 gross 8-32x§ Brass Machine Screws 2 1 1 gross 6-32 Brass Nuts 40 ea. 166 ea. 41 ea. 3 ea. 2 ea. 160 ea. 120 ea. 120 ea. 40 ea. 80 ea. s/a" Rubber Gromments 2 Circuit Normaled Jacks. 3 Circuit Jacks’ 2 Circuit Double Plugs 3 Circuit Plugs‘ 5.3 mh. 14 ohm Choke Coils .015 uf 1200 volt, 2% Mica Condensors‘ .001 uf 600 volt, 2% Mica Condensors' Bakelite Mounting Strips‘ Stand-Off Mountings, 1" ° ' Available from present Government Surplus Stocks -23.. 0‘ $3.qu .uitssszxfim \uioxuz 3 gm. =2 um :26 L 1A m\ km in lWa LIWNIIIQWNFILIIIIH lwcolll , i i. i- if L .,, w: IAvllnfi lAvl VI ..“.1 Av! he a USN mg on $52.0 29: .5050 m\.o\< autumn: 7 «a. «scum. = 2 a Oi $235 to: .35.}. 26% \cZoxuz newsman" .7 s ass» 3‘ ">13; 3 O 3 w Q Q tJrJNITTjth w on I? a, * PIP _ MLLIO Oirlo . % _ 0:4 ._- _ IgoL in: H lufl OI: l Incl _ a a if}. lumnwllllrlumarl! 9.36»an \utol \ , ‘ \ 35$ sisal, Vacuum *comx gmsaasuay CHAPTER IV Tests and Results 4.1 Voltage and Current Measurements The following data show the results of voltage and current measurements at the end Of each section for various frequencies under Open and short circuit values Of termination. The resulting standing waves are clearly shown. Possibly more data than necessary has been taken to show this result but it is all included here to show that there are no discontinuaties or irregular Operation points on the line. Voltage and Current Measurements f=500 cps. Section Open Circuit Short Circuit 11 12 V 11 12 V 0 32.0 32.0 25.0 28.0 28.0 25.0 1 29.0 29.0 27.0 30.6 30.6 22.0 2 25.0 25.0 28.8 32.5 32.5 19.0 3 21.2 21.2 50.0 34.0 34.0 16.0 4 17.3 17.3 32.0 36.0 36.0 13.0 5 13.3 13.3 33.0 37.2 37.2 10.0 6 9.0 9.0 33.6 38.0 38.0 6.3 7 4.5 4.5 33.8 38.5 38.5 3.2 8 0.0 0.0 34.0 39.5 39.5 0.0 -31- f=796 cps. Voltage and Current Measurements Section Open Circuit Short Circuit 11 12 V 11 12 V 0 79.0 79.0 25.0 12.1 12.1 25.0 1 73.5 73.5 33.0 15.8 15.8 23.0 2 66.4 66.4 41.0 19.0 19.0 21.0 3 58.1 58.1 47.8 23.3 23.3 18.0 4 48.0 48.0 51.5 26.0 26.0 15.0 5 37.0 37.0 58.0 28.2 28.2 12.0 6 25.1 25.1 62.0 30.0 30.0 8.0 7 12.9 12.9 64.5 31.2 31.2 4.0 8 0.0 0.0 65.0 31.9 31.9 0.0 -52.. Voltage and Current Measurements f=12OO Ops. Section Open Circuit Short Circuit 11 12 V I1 12 V O 79.0 79.0 25.0 12.0 12.0 25.0 1 83.0 83.0 14.0 6.4 6.4 25.8 2 81.8 82.0 13.8 7.2 7.2 25.0 3 75.2 75.1 30.9 13.0 13.0 23.6 4 66.5 66.5 44.2 18.6 18.5 20.2 5 54.0 54.0 53.0 24.2 24.2 16.3 6 38.8 38.8 58.0 28.8 28.8 11.7 7 20.0 20.0 62.0 31.1 31.1 6.0 8 0.0 0.0 63.0 32.2 32.2 0.0 -33.. Voltsge and Current Measurements f=2500 Ops. Section Open Circuit Short Circuit 11 I2 V 11 I2 V 0 31.8 31.8 25.0 32.2 32.2 25.0 1 14.9 14.9 33.0 42.5 42.6 12.0 2 11.5 11.5 34.0 43.1 43.1 9.0 3 28.7 28.6 26.0 34.0 33.9 21.0 4 40.0 40.1 13.0 17.7 17.7 30.5 5 43.0 43.0 4.0 5.7 5.7 33.0 6 36.2 36.2 18.0 24.0 24.0 27.9 7 20.1 20.1 29.0 37.2 37.3 12.9 8 0.0 0.0 33.8 42.0 42.0 0.0 Voltage and Current Measurements f=3500 eps. 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The circuit of Figure a) being used when the line is capacitive in nature and that of Figure b) when the line is inductive in nature. A very good idea of the value of the Character- istic impedance can be obtained by first calculating the characteristic impedance of one of the H sections. 203’; :VKflJlJL 7 6¢JB y VhiZthfizfiZ£é§hmiJ o r J 61/7177(x.o¥ix»'3 7oz [’/¢/‘ --46-- ZQ_ Calculations for Eight Sections freq. Zoo x ch Z0 9 600 1440 x 454 805 ~15.5° 500 722 x 804 740 ~12.9° 796 282 x 1940 740 -8.7° 900 180 x 2970 750 -7.8° 1000 — - 1100 191 x 2820 735 -5.3° 1200 268 x 1791 695 —3.3° 1500 756 x 722 730 -5.7° 1700 1305 x 587 710 -6.3° 1900 2640 x 172 674 -7."0 2000 - - 2200 1895 x 264 694 -4.7° 2500 726 x 704 716 -5.0° 2900 214 x 2060 664 -3.7° 5000 - - 3200 278 x 1651 677 —0.2° 3500 669 x 672 670 +0.1° 3800 1523 x 262 655 O.6° 3900 2195 x 196 654 0.3° 4000 - — 4200 1595 x 515 652 1.5° 4500 528 x 790 646 l.9° 4700 305 x 1541 640 0.9° ...49... .I'lhd‘uNaIE'iHI . p 3 “I'll. .. . 9 Qpen Circuit Measurements for Eight Sections freq. R Lmh Z Zmag Zarg 500 105 750 105 -31450 1440 -82.2° 500 110 225 110 - 3720 722 -81.5° 795 118 51 118 — 3255 282 ~55.5° 900 128 25 128 - 3125 180 -44.7° 1000 127 2 127 — 315 128 -5.8° 1050 110 5 110 + 340 117 19.7° 1100 152 15 152 + 3100 191 51.5° 1200 159 29 159 + 3215 258 55.50 1500 555 59 555 + 3555 755 52.2° 1700 705 105 705 +31100 1505 57.2° 1900 2255 115 2255 +3157o 2540 51.50 2200 1155 110 1155 431520 1895 -55.2° 2500 274 45 274 - 3572 725 -57.9° 2900 172 7 172 - 3127 214 —55.4° 5200 190 10 190 + 3202 278 46.8° 5500 520 25 520 + 3587 559 51.4° 5800 1140 42 1140 +31008 1525 41.4° 5900 2005 57 2005 + 3892 2195 24.00 4200 954 58 954 -31000 1595 -46.8° 4500 500 15 500 — 3455 528 -55.4° 4700 220 7 220 - 3211 505 -45.8° 4900 190 2 190 - 352 200 -17.9° -48- Short Circuit Measurements for Eight Sections freq R Lmh Z Zmag Zarg 500 285 188 285+ 3554 454 51.2° 500 455 212 455 + 3662 804 55.5° 796 1295 288 1295 +31440 1940 48.0° 900 2585 240 2585 +31450 2970 29.2° lOOO _ - 1100 2090 277 2090 ~31890 2820 -42.1° 1200 915 211 915 -31590 1791 ~60.1° 1500 204 74 204 - 3692 722 —75.6° 1700 154 55 154 - 3564 587 -69.8° 1900 117 10 117 - 3120 172 -45.8° 2000 - _ 2200 171 14 171 + 3202 264 49.8° 2500 551 40 551 + 3628 704 62.0° 2900 1806 55 1806 +31000 2060 29.0° 5000 — - - 5200 1124 60 1124 ~31210 1651 ~47.1° 5500 520 27 520 - 3591 672 -61.6° 5800 200 7 200 - 3169 262- -40.2° 5900 180 5 180 - 3 78 196 -25.5° 4000 - _ 4200 202 9 202 + 3259 515 49.8° 4500 406 24 406 + 3680 790 59.2° 4700 956 55 956 + 3960 1541 45.7° . o . 1 A n . . 1 o I ‘3 I n _ . 1 1 . r 1 a . . w . . . . 1 A? 11‘... a c v E O ' f f “ *7 1 ‘1 £933 . 1w ' $9229; 57 (/17 . l I ~$w » t o .~+—1 ”uh- I.. a 5 I n . r\ a .... .... 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III?!» 4.5 Determination of the Line Constants from Impedance Measurements Often it is desirable to obtain the constants of an unknown line. A very convenient method of doing this is from the impedance data gathered in section 4.2. The following set of calculations will then determine the line constants. They are used here also as a check upon the impedance measurements since we know their actual values. . ; aw II 7?5 Clo/b r J / (I 20¢ .2}; Agata ° 25:, : /77/§M0 I?" 9‘13,» - E; = #211447” A. 7fi/é Z~ 341‘ ‘5 U 20 H WI! =/.Z~s_c_ rWfl 5“ Mr t 2042 421/6 = / 4%2 +J 147' A=Myz B: .2./7 A 2716 1 = ..zaw 7.7? _. [/75 is! (xi/=91; 7 M 6044‘5‘ 2i; 2 ,3// 0241:,3/7 u = -/73 - ./73 d - ~7— =,d-2€// /W H .29 : 2.35 7:“ Jfl/ #0995”) —- .71 THY/)7 2g? : az/ye’ :/{/fl.]//0 8!: 7p. Eg’Fd‘o= [lite/M _ 1.2M 6" f -,—. ./d'52//Ld///W% rzd+6<3 ':.02‘f//-/Jt/J—5'z -. , /é.J—J-L&Z6 Z: 20 r: 7ygg~ffidx,/¢a‘1/Z/d : //¢//_M" = 35,2 fJ/d? E: 3;,2a4w/W L 3 ‘2‘}‘7: J/7f/x4/W 7, 2 j: _ marffl/J g _ ° 75/aA/Zéf" ‘2. - Dddcl/O Ami-0 "-' oaooao3¥ fJ,Ma.z/0 G 3 3’5/ JL/bfi/é/W \ ...Z (3 "' 9551/0 2 ,é‘S/fi Joy/@6021»: IT .5 (“if 2 V/W “(3' Mail ,9! .. W1 :3026flflW/aa >5 V: (<7 “ ,/a‘31 L: [I flW 54$ .Z/aZ 'M/f ’70 ”51579 1,7/Z /.2,JZ 4.4 Location of Faults The usual method of location of fault on a trans- mission by accurate bridge measurements is not dis- cussed here due to lack of time and space. This method is well known however and there is no reason to believe that it would not work nicely with the artificial line. Another more usual method of location faultshaas used however. This method is employed very little if at all at the present time,however its great advantages seem to warrant widespread future use in all types of transmission lines. Briefly the method consists of sending a very sharp pulse type signal down the transmission line. If the line is terminated in the Characteristici Impedance, the pulse is dissapated and reflections are not present. However, if the line is not properly terminated or a fault exists, a pulse is reflected back to the start of the line. With a series of repeating pulses, an Oscillo— scope can be placed across the line showing the applied pulses sweeping across the screen Just as in viewing a sine wave. If reflections are present, they will be shown displaced from the sending pulse by an amount prOportional to the distance of the fault causing the reflection. .. 60-. If the frequency of the pulse is known, and the apparent velocity of the wave on the line is known, the distance to a fault is very easily calculated from measurements taken upon the oscilloscOpe screen. A very complete knowledge of the type of fault which exists is also known. From the above diagram the time to the reflected wave can easily be found since T1 is known from f. Perhaps the best way to find the apparent velocity of the line is to place a discontinuity on 'the line at a known distance and measuring the time and hence the velocity from vs f3 . Knowing this) the fault can be located by 2/=V=Yf /Z : «L: ”N -51- On the following page is a circuit diagram of this method of determining line faults. The source of pulses comes from a square wave which is differen- tiated by the R—C combination. The 650 ohm 6db pad is placed in the circuit so that Z is more nearly 8 matched to 20 . This prevents another reflection from occuring if a wave comes back toward Z8 . The following pictures were taken from the screen of a standard 5“ DuMont oscilloscope. A plate type camera with an auxillary lens to permit close—up foucing was used to take the pictures with an exposure of approxi- mately 2 seconds on Super XX film. Picture a) is that of a normal line. The slight waves or uneveness of the pulse are believed to be small reflections caused by lumping the line constants. By eXpanding the vertical axis of the oscilloscOpe greatly, 8 uneven places occur at approximately the right distance to account for this fact when 8 sec- tions of line were used. Picture b) is that of an Open-circuited line on the eighth section. The reflected wave is clearly seen. Picture c) is that of a short circuited line on the eighth section. The reflection is of the Opposite polarity to that of the Open circuit but is in exactly the same place and of the same form. Picture d) is of a normal line but with two 50 ohm -52- fiflwmusfl 14331.: 33:4 .3 mama < m! $330 . 3.6.35 m kom owe-$8 1cm rigor t3..5 36} 93an 2: 4 403...?» neigkotfi .N HHHM H _ e ii. 0 Normal L/ne O/oen C/rcuI/ on Sec/Ion No.8 Shor/ C/rcal/ on Sad/on No. 8 /00-¢ fi’eew/anm do/a/aol on Sec/hm 4/05 resistors inserted into the line at the end of the sixth section. Compare this photograph with that of the normal line and the reflection caused by the resistors is easily seen. The calculations to determine the placement of the resistors follow. 7% H,“ ”2,57%,” ”if/73% T. Y: ‘z/KX/dldx 7% : 239/15 WM = V7‘ ~ 27y16 // j, IZ Z ‘ "—“f ”.232 A/aao .-.- d17é/W C/w/ylf/ (.00 Axis/7;»: W /ZW With very simple equipment and a little practice this method of determining line or cable faults is quite accurate and informative. For the best results the following things should be tabulated on the lines to be tested. 1. Velocity of prOpogation of the line 2. A normal picture of the line Another use for this type of testing of transmis- sion lines is that of correctly terminating the line. Observation of the oscillosc0pe while varying the terminating impedance at the end of eight sections of 8 line would show a very definite reflection if the terminating impedance was varied 5% from 20’ A simple test like this would easily and quickly eliminate the echo effect caused by reflection in the transmission of pictures by wire. -67... 4.5 Square Wave Testing The frequency response of a circuit can easily and quite accurately be determined by Square Wave Testing. A Fourier analysis of a square wave gives the following result e= 7‘; (ad-éaamégiw gawk“) Since the square wave contains almost every conceivable frequency, it can be applied to a network and the dis- tortion of the wave observed on an oscilloscope. PrOper interpretation of this output wave will then determine the frequency reaponse of the network. Time does not permit an accurate analytical analysis of square wave testing in this paper, however a very good idea of the frequency response of a network can be made observing the output wave and comparing with the wave form known to exist in the extreme cases. Also, several sources list picturesuof waves with which an unknown can be compared to obtain an idea of the frequency reaponse. If a square wave is applied to a network with poor low frequency response, the output will be similar to the following where the dotted line is the square wave input. If a poor high frequency reaponse is present, the output wave will be similar to the following. Many times it is desirable to observe both the input and output waves on the oscilloscOpe at the same time as shown in the above drawings. This is accom- plished by the use of an electronic switch which rapidly applies first one voltage then the other so that they both appear on the y axis. The accompanying photographs show the square wave response for 8 sections of artificial line for frequencies of 500 and 2000 cycles per second. The 500 cycle per second photograph shows the characteristic of excellent low frequency response. High frequency deficiencies are not apparent. The small oscillation at the peak of the wave is due to a peak in the response curve or a rapid cut off frequency. Since our H section is also one of a low pass filter, we can eXpect a cutoff frequency to occur. The frequency can be measured from the photograph by a proportion. c740,; / , a: 3' m, ova 76%47Qw436a/ -59- Zflflé (”ya/6’s fier Secom/ The frequency of a cut-off calculated from filter theory is as follows and shows very good agreement with that actually found. 1'“ / ‘Fc‘ /7' ,Lc '- 'I' ,5 / fl l/J/JJ/o'JX. o/IJM’ d / a, 3M ?;Cga/Aw The second smaller oscillation at first appears to be of doubtful origin. I believe this oscillation to be caused by a reflection of the initial surge back toward Zg and a consequent reflection back into the line. Zg was not matched to the line while square wave testing and this error in carrying out the eXperiment I feel is certain to be the cause of this unexpected oscillation. The dismantling of the artificial line to install slightly different induc- tances prevented taking further data to fully account for this phenomenom. The 2000 cycle per second photograph shows a ' definite high frequency deficiency in the output wave. This is determined from the slanted vertical lepes. The oscillation is still evident by the rough peak but is not quite so easily calculated. A more involved IZ analytical treatment would give the frequency however. ~71~ CHAPTER V Conclusion This paper does not intend to be a complete works on transmission lines. It describes the design, con- struction, and testing of an Artificial Transmission Line to be used in the Laboratories of the Electrical Engineering Department of Michigan State College. The theory presented has been used to justify the cal- culation of the elements used and to explain the re- sults of the tests. It was intended to construct 40 sections of artificial line which would be the equivalent of 251 miles of a pair of 104 mil wires spaced 12". However, considerable difficulty was experienced in obtaining delivery of the necessary inductors. Eight sections were constructed with the available coils which made 46 miles of equivalent Open wire line. Tests were run on the completed 8 sections. Since we were unable to obtain a complete order of 160 coils similar to those used in the first 8 sections, it is necessary to replace the coils used in these sections with a type which could be obtained in sufficient quantity to complete the line. The coils used had 9 ohms resistance and those available in sufficient quantity have 14 ohms resistance per coil. This new coil will offer a closer approximation to the resistance of an equivalent amount Of Open wire. All tests taken on the line agree with the expected results very closely. The entire character— istics of the equivalent open wire line are not avail- able at the present time so that an absolute check cannot be made. The checks available are quite satis- factory though. The mechanical construction Of the line lends itself very well to measuring the electrical effects. Faults of different kinds can easily be placed on the line for future laboratory students to find. Several additional tests could be applied to the artificial line. Time did not permit their being used in this paper but will be mentioned for possible future use. A few are Determination of the Phase-shift’3' Along the Line, Location of Faults by the Impedance)"l Method, further investigation of the Location of Faults by the Pulse Technique described in this paper. The line seems to be very well adapted to the study of transient effects within the limitation of the voltage breakdown point Of the condensers used. -73- 9. 10. 11. 12. 15. 14. References Artificial Electric Lines by A. E. Kennelly, page 3,636Graw-Hill Insuline Corporation Catalogue Communications Engineering by W. L. Everitt, pageVBQ, McGraw-Hill Hyper and Ultra High Frequency Engineering by Sarbacher and Edson page'321, John Wiley Communicatiog Networks, Volume NO. 2 by E. A. Guillemin, page 259, John Wiley Netwogk Analysis by H. W. Bode, page 268, D. Nostrand Radio Engineers Handbook, by F. E. Terman, page 268, McGraw-Hill Expgriments in Electronics and Communicatiqg Engineering by Schulz and Anderson, page 551 Experiment NO. 462.09 E.E. 451b, 1947 Electronics 17 Pt.2 November 1944 page 110 Radio Engineers Handbook, by F. E. Terman, McGraw Hill, page 968 Ultra High Frequency Technique by Brainerd, ioehler, Reich, Woodruff, page 46, D Van Nostrand Ultra High Frequency Radio Engineering by W. L. Emery, page 115, Macmillan Experiments lg Electronics and Communications Engineering by Schulz and Anderson Communications Engineering by W. L. Everitt, page 154, MoGraw Hill Bibliography Artificial Electric Lines by Kennelly, McGraw Hill Artificial Transmission Line by Bartlett Radio Engineers Handbook by Terman, McGraw Hill Ultra High Frequenqy Radio Engineering by Emery Macmillan Network Analysis and Feedback Amplifier Design by H.#W. Bodie, D. Van Nostrand Ultra High Frequency Techniques by Brainerd, Koehler, Reic , \OOdruff, D. Van Nostrand H car and Ultra High Frequency Engineering by arbacher and Edson, Wiley Communications Engineering by W. L. Everitt, McGraw- Hillfi Experiments in Electronics and Communication Engineering B? Schulz and Anderson Princgples 3: Transmission 13 Telephony by M. P. Wainbach ' Magazines American Institute 22 Electrical Engineers Electronics MICHIGAN STA‘I'E UNIVERSITY LIBRARIES III] III" III lljllll III!“ I 31293 03 75 5261