Tijdschrift van het
Nederlands Radiogenootschap
DEEL 22 No. 6 NOVEMBER 1957
Introduction
The ta sk of the D r. N e h e r L a b o ra to ry as c en tral la b o ra to ry of the N e th e rla n d s P o sta l and T elecom m unications Services is to perform the developm ent w ork on b eh alf ot the v arious branches of P T f, and to do research w o rk in some lim ited fields.
In the p re se n t age of re v o lu tio n a ry p ro g ress in technics and science, w e should of course end eav o u r in the in te re st of the ra p id ly expanding services, to recognize the fu tu re tren d of technical and scientific developm ent.
T h erefo re it is an im p o rtan t fe atu re of th e lab o rato ry 7^ ta sk to follow an d stu d y these new developm ents an d to keep in view the possib ility of applying new w orking-m ethods in the P o sta l and T elecom m unications S ervices w ith its m any aspects. M a n y an d various indeed, fo r th e y com prise i.a. telephony, teleg rap h y an d telex, bo th w ith re g a rd to transm ission via c a rrie r cables o r via radio, and w ith re g a rd to sw itching techniques an d equip
m ent. The m any problem s to be d e a lt w ith re fe r to equipm ent for rad io b ro ad castin g an d television, to p o sta l m echanisation, to the intro d u ctio n of autom ation in the P o sta l C heque and C learin g Service, and to the use of com puters lo r d a ta p ro cessing. I t is c lear th a t system engineering, too, form s a field of action fo r the L a b o ra to ry .
W ith a lim ited scientific sta ff the L a b o ra to ry trie s to ac
com plish all these ta sk s to the b e st of th e ir abilities an d it is g ratify in g to note th a t the p re se n t issue of the ’ T ijdschrift van het N ed erlan d s R ad io g en o o tsch ap ” has entirety been devoted to co n trib u tio n s of some of the L a b o ra to ry ’s staff. I hope th a t these a rticles w ill give the re a d e rs an insight into the w ork done a t the D r. N e h e r L a b o ra to ry and m ake them in te re ste d in it.
The H ague, O c to b e r 1957.
D ire c to r G en eral o f th e N e th e rla n d s P T T .
320
M a q u e tte P T T la b o ra to rie s a t L eidschendam .
T he in te rio r o f the rig h t-h a n d h all sh o w in g the w o rk room s.
N ovem ber 1957 - Deel
22
- N o6
321Som e problems concerning the choice of cable-circuits for television transm ission
by A. P. Bolle *)
Summary
In this a rticle som e problem s concerning th e choice o f c ab le-c ircu its fo r television transm ission a re discussed. T y p ic al ad v an tag e s an d d isa d v a n t
ages of the sym m etrical a n d asy m m etrical circu its in re la tio n to television tran sm issio n a re show n.
T h e resu lts of these co n sid eratio n s a re ap p lie d to the d ifferent p o ssib ili
ties o f television transm ission system s.
1. Introduction.
I t can be show n, th a t fo r the television system (625 lines, 25 pictures p er second) ap plied in the N e th e rla n d s an d also in m any o th e r countries, th e highest frequency am ounts to ab o u t 5 M c/s. The lo w e st freq u en cy is 25 c/s, a p a r t from the dc- com ponent in the signal, w hich com ponent can be re -ad d ed to th e signal a t an a r b itr a r y point in the chain b etw een cam era and receiver.
D ue to th is larg e re la tiv e b an d w id th (25 c/s —
5
M c/s) high dem ands a re m ade on the transm ission medium, especially if a cable is chosen as such. F o r the frequency ban d w hich can be used on cables usu ally lies u n d er 12 M c/s, (except in the case of very sh o rt connections, w hich are n o t d e a lt w ith here), because of the fa c t th a t the a tte n u a tio n of a cable expressed in dB increases a t le a s t w ith the sq u are ro o t of the frequency. This m eans th a t on cables a television signal can be sen t eith er as a video-signal (i.e. unm odulated 25 c/s —5 M c/s), o r am plitude- m odulated on a c a rrie r the freq u en cy of w hich has been chosen in such a w ay th a t bo th sid eb an d s o r one com plete sid eb an d and one vestigial sid eb an d are u n d er 12 M c/s. E ven in the second case the re la tiv e b a n d w id th is large. W ith rad io -tran sm issio n th e re are fe w e r difficulties in th is resp ect, because of th e fact th a t higher frequency-bands can be chosen. A s a resu lt, the) T ransm ission B ran ch .
322 A. P. Bolle
re lativ e b an d w id th is fa r sm aller th a n in the case of cable- transm ission. In some cases a higher freq u en cy -b an d is chosen even on cables, in o rd e r to obtain a sim ple m odulating a p p a ra tu s an d a less larg e re la tiv e b a n d w id th .2. Transmission requirements.
The transm ission req u irem en ts w hich m ust be m et can be d eriv ed from the fa c t th a t fo r a good p ictu re-q u ality it is n ecessary th a t the tim e-dependency of th e o u tp u t-sig n al should ap p ro x im ate the tim e-dependency of the input-signal of the transm ission-m edium . From this it follow s th a t the p h a se -fre quency c h a ra c teristic p la y s as im p o rta n t a role as the a tte n u atio n -freq u en cy ch aracteristic. T his is in c o n tra st w ith telephone- transm ission p ractice. In ste a d of describing the transm ission p ro p e rtie s w ith the aid of the above-m entioned tw o c h a ra c te r
istics, it is also possible to do so by m eans of the so-called pulse-response o r w ave-form response. B oth m ethods are id en ti
cal, as is w ell know n, b u t since the television-signal itse lf con
sists of a g re a t num ber of successive voltag e-step s, corresponding to v ariatio n s in lucidity, the la st m ethod is ad v an tag eo u s in th a t it gives m ore d ire c t inform ation a b o u t the b eh av io u r of the transm ission-m edium . The C .C .I.T .T . has form u lated a num ber of provisional req u irem en ts fo r the transm ission c h aracteristics as w ell as fo r the w ave-form -response [
1
].I t is im p o rta n t th a t the cable used should have a good im
pedance re g u la rity . T he re su lt of too larg e an im pedance ir re g u la rity is, th a t a fte r recep tio n of the w a n te d (p rim ary ) signal a m ore o r less g re a t num ber of seco n d ary signals (G erm an : MitfLuss, D u tc h : nasleep) are received w hich cause the so annoying m ultiple p ictu res (ghosts). T he C .C .I.T .T . basing itself on the w o rk of K a d e n [2] an d F u c h s [3] has fo rm u lated the req u irem en ts fo r the im pedance re g u la rity w hich can be checked e ith e r b y s te a d y -sta te m easurem ents o r b y pulse m easu re
m ents [1], B ased on the sam e phenom enon th e re is also a re quirem ent fo r the m inim al adm issible re tu rn loss b etw een the cable-im pedance an d the in p u t and o u tp u t im pedance of re p e a te rs .
I t is ev id en t th a t th e re is also a req u irem en t fo r the signal- to-noise ra tio ; as w ell fo r continuous random noise as fo r periodic noise [
1
].A ll the C .C .I.T .T . p rovisional req u irem en ts a re given fo r a 2500 km in te rn a tio n a l h y p o th etical reference circuit fo r television
The choice of cable-circuits for television transmission 323
transm ission. Till now only little experience h as been gained as re g a rd s the contrib u tio n s m ade by each of the co n stitu en t p a rts of the reference circuit to the to ta l adm issible deviation from the id eal case.3. Possible cable circuits
T here are tw o so rts of circuits; nam ely the sym m etrical an d the asym m etrical circuits. A circuit is sym m etrical w hen b o th conductors have the sam e electrical position w ith re sp e c t to e a rth . In the m any form s of telephone cables a m ore or less g re a t num ber of sym m etrical p airs are p resen t. The phantom circu it w hich can be m ade from tw o sym m etrical p airs (the side circuits) w hen these p airs to g e th e r form a q u ad -stru ctu re, is also a possible sym m etrical circuit fo r the transm ission of television signals. In m ost cases th ese circuits are p ap er-in su lated . D ue to the losses in the p ap er, the ra te a t w hich the a tte n u atio n of the circu it in creases is m ore th a n p ro p o rtio n a l to the square ro o t of the frequency. O f la te a cable ty p e w ith a b e tte r so rt of insulation m aterial (e.g. poly-ethylene) has come into use. In such cables the a tte n u a tio n increases p ro p o rtio n al to th e sq u are ro o t of the frequency as a re su lt of the fa c t th a t the losses occur p ra c tic a lly exclusively in th e conductor m aterial. T his is a g re a t ad v an tag e, especially w hen these cables are used fo r high frequencies (e.g. television transm ission).
T here is little to be said ab o u t the im pedance re g u la rity of the sym m etrical circuit. I t is reaso n ab le to suppose th a t w ith cables having p lastic insulation the im pedance re g u la rity is g re a te r th a n w ith those having p ap er-in su latio n , because of the b e tte r geom etrical co n struction. F o r sh o rt distan ces the requirem ents becom e less strin g en t. I t is possible th a t even the older p ap er- in su lated circuits give sa tisfa c to ry re su lts in those cases.
The coaxial circuit is the m ost used asym m etrical circuit.
T here are tw o ty p e s, one w ith solid insulation (poly-ethylene) an d one air-in su lated . F o r b o th ty p e s the a tte n u a tio n increases p ro p o rtio n a l to the sq u are ro o t of the frequency. T he im pe
dance reg u la rity of the la tte r type is b e tte r th a n th a t of the first. If a coaxial circuit w ith solid dielectricum fo r v e ry long distan ces is used fo r television transm ission, some difficulties m ay arise. A s a rule sev eral coaxial p airs are covered b y one sh eath ju s t as w ith sym m etrical circuits.
E ach of the tw o circuits (sym m etric an d coaxial) h as its ow n specific ad v an tag es an d d isad v an tag es.
324 A. P. Bolle
T he a d v an tag e of th e sym m etrical circuit is th a t it is m ore insensitive to asy m m etrical in terferen ce from outside (m ains hum, stro n g tra n sm itte rs). Sm all d istu rb an ces in the sym m etry give rise to the p e n e tra tio n of the in terferen ce into the w an ted signal. A d isad v an tag e of sym m etrical circuits is th a t th e y influence each o th e r (c ro ssta lk ) especially a t high frequencies w hen th ere is no screen. A s a rule the c ro ssta lk in creases w ith the frequency. T here a re com pensation m ethods, w hich a re, h o w ever, n ev er p erfect. A s a m a tte r of fa c t the c ro ssta lk determ ines the h ig h est adm issible frequency on sym m etrical circuits. A s a rule, fo r th e successful ap p licatio n of sym m etrical! circuits a t high frequencies it w ill be necessary to m ake a sufficiently good screen aro u n d each sym m etrical p air. N a tu ra lly , th is is n o t w ith o u t influence on th e a tte n u a tio n an d the price.
W ith the p h antom -circuits the conditions are m ore fav o u rab le.
T he constru ctio n of th e q u ad being ideal, the e x te rn a l field of thejj p h an tom -circuit is very sm all. A s a re su lt the cro ssta lk b etw een phantom -circuits w ill be less th a n w ith the side-circuits.
U n d er th ese ideal conditions the screening can be om itted. The q u ad configuration, how ever, is n ev er p erfect. The deviation from th e id eal construction is la rg e r as the con d u cto r d iam eters a re sm aller an d it is la rg e r in p ap e r-in su la te d cables th a n in poly-eth y len e-in su lated cables. The ad v a n ta g e of the phantom - circuits is com plete, w hen no use is m ade of the side-circuits.
The c ro sstalk b etw een the side-circuits an d “ th e ir" phantom - circu it is fa irly large, w h e re a s th e com bined use of th e side- circuits an d phantom -circuits m akes the presence of com plicated provisions n ecessary, especially a t high frequencies.
T he ad v an tag e of th e coaxial p a irs is th a t the c ro sstalk d ecreases w ith th e freq u en cy because of th e fa c t th a t the o u ter con d u cto r acts as a screen. A t lo w er frequencies (below say, lO O kc/s) the screening becom es insufficient as a rule. T he use of a coaxial p a ir fo r th o se frequencies m ay be dan g ero u s. The sam e holds w ith re sp e c t to the p e n e tra tio n of asym m etrical in terferen ces. T hese phenom ena can be red u ced to a m ore or less larg e e x te n t by m aking an ad d itio n a l screen o r b y p re v e n t
ing th e flowing of cu rren ts, induced from th e outside, into the o u te r conductor. T hese cu rren ts cause a v o ltage d ro p on the inside of th e o u te r conductor, especially a t low frequencies.
A s a re su lt a c u rre n t arises in the coaxial circuit, w hich c u rre n t can n o t be s e p a ra te d from th e w a n te d signal. T he flow ing of th e above-m entioned c u rre n ts can be p re v e n te d to a m ore or
The choice of cable-circuits for television transmission 325
less larg e ex ten t by in sertin g a high im pedance into the o u ter conductor. H o w ev er, th is high im pedance should n o t be p resen t fo r the w a n te d cu rren ts. This can be done b}r w inding the inner an d o u te r conductor to g e th e r on a core. In this w a y the so-called coaxial coil comes into existence, w hich coil introduces into th e coaxial p a ir some ad d itio n al atte n u a tio n . The in te rru p tio n of th e o u te r conductor can also be reach ed b y inserting a tran sfo rm er. This can only be done if th e relativ e b an d w id th of the w a n te d signal allow s the co n stru ctio n of a tra n sfo rm e r w ith good transm ission p ro p erties
T he a tte n u a tio n of the differen t circuits m ust also be con
sidered. F o r all circuits it is possible to choose the dim ensions in such a w a y th a t the a tte n u a tio n has a minimum value. A s
sum ing th a t th e a tte n u a tio n arises from losses in the conductor only an d th a t b o th conductors are m ade from copper, the re sults are as follow s [d ]:
a. T he sym m etrical p a ir (w ith screen) h as a d ia m e te r w hich is 1.63 tim es as larg e as th e d iam eter of a coaxial p a ir fo r the sam e atte n u a tio n . The q u a n tity of co p p er is 1.3 tim es as large.
b. T he p h an to m -circu it (w ith o u t screen) w ith th e sam e o u t
side d iam eter as the C .C .I.T .T . coaxial p a ir («s; 10.5 mm) has an a tte n u a tio n w hich is 1.3 tim es the a tte n u a tio n of th a t co
ax ial p a ir an d needs only h alf the q u a n tity of copper. I t is tru e th a t b o th side-circuits have a lo w er a tte n u a tio n th a n the p h a n tom -circuit (a b o u t
1 0
% low er), b u t th e y need a screen in o rd e r to m ake the use a t high frequencies possible. A s a re su lt the atte n u a tio n increases co n sid erab ly ( ^ 5 0 % higher th an C .C .I.T .T . coaxial pair). The q u ad stru c tu re being n o t ideal, a screen is necessary an d consequently th e a tte n u a tio n and the q u a n tity of copper increase.From the foregoing it follow s th a t w ith re sp e c t to the in
sen sitiv ity fo r low -frequency in terferen ces the S
3
m im etrical circuits (even w ith o u t screen) are by fa r superior. The id eal phantom -circuit also has a good in sen sitiv ity fo r high-frequency in terferences. The deviation from the id eal case being too large, th e presence of a screen is n ecessary an d as a re su lt the phantom - circuit is su rp assed by each of the side-circuits (lo w er a tte n u a tion, less copper). The increase in a tte n u a tio n is considerable, how ever, and th erefo re the coaxial circuit is su p erio r in this resp ect.
F o r a com plete com parison of th e different possibilities,
326 A. P. Bolle
m any o th e r fa c to rs m ust be c o n sid e re d : price an d q u an tity of th e dielectricum , n ecessary am ount of screening, m anufacture difficulties etc. etc. In each case it is n ecessary to consider w hich ty p e of circuit m ust be chosen.4. Transmission systems
I f television signals are to be tra n sm itte d ov er sh o rt d is t
ances, th e y can b e st be tra n sm itte d unm odulated, in o rd e r to avoid the use of expensive m odulating equipm ent. B ecause of th e freq u en cy -b an d involved th e sym m etrical circuit is p re fe rred . If a g re a t in sen sitiv ity a g a in st high-frequency in terferen ces is desired, a screen is necessary. A n ad d itio n al ad v a n ta g e of the sym m etrical circuit is th a t com pletely b alan ced am plifiers can be used because it is n e a rly im possible to c o n stru ct a tra n sfo rm e r w ith good tran sm issio n p ro p erties. W ith b alan ced am plifiers it is very easy to avoid the coupling via th e supply-voltage sources. W ith u n b alan ced am plifiers th is coupling can n o t be avoided com pletely in view of the lo w e st frequencies involved.
^V ith the b alan ced am plifiers it is also possible to avoid the cathode an d screen grid decoupling condensors.
B ecause of th e v e ry larg e relativ e b a n d w id th th e e q u alisa
tion of the a tte n u a tio n an d p h ase is fa irly com plicated.
If television signals are to be tra n sm itte d over larg e d ist
ances, it is ev id en t th a t th ey m ust be m odulated. T he C .C .I.T .T . has recom m ended a vestig ial sid eb an d system w ith a c a rrie r frequency of 1056 kc/s. T he m odulation a p p a ra tu s is com plicated.
The lo w e st freq u en cy involved is such th a t a coaxial cable can be used.
In G erm an y a n o th e r system h as come into u se : a double sid eb an d system w ith a c a rrie r freq u en cy of 21 M c/s [5]. T h e re fore the re la tiv e b a n d w id th (16 M c/s — 26 M c/s) is r a th e r sm all.
T he m odulation equipm ent seem s to be fairly sim ple. A s a resu lt, th is system can be used fo r sh o rt distan ces on the C .C .I.T .T . coaxial cables w ith a re p e a te r spacing of a b o u t 4.7 km. T he eq u alisatio n of th e a tte n u a tio n an d p h ase is easy.
5. Bandwidth-reduction
A ll tran sm issio n p roblem s becom e less com plicated w hen the b a n d w id th involved can be reduced.
W ith very good D C -re s to re rs it seem s to be possible to
The choice of cable-circuits for television transmission 327
om it from the video-signal the freq u en cy b an d below , say, lO k c/s [6
].T he design of a v id eo -tran sfo rm er becom es easier in th a t case.
T he a d v an tag es of such a tra n sfo rm e r are ev id en t: im pedance- tra n sfo rm atio n a t th e in p u t an d o u tp u t stag es of am plifiers, a change from balan ced to unbalanced circuits etc. etc.
W ith some form s of coding it is also possible to om it a g re a t d eal of the high frequenc
3
"band of the video-signal [7].T his is, from the p o in t of view of the tran sm issio n engineer, also very a ttra c tiv e . As fa r as the p re se n t a u th o r know s the tw o reduction m ethods a re b ased only on th e o re tic a l con
sid eratio n s an d n eith er has been applied in p ractice.
Literature.
1) C C IF 1955/56 — SG 3 Docum ent no 77, pp. 20—62.
2) H. K a d e n : T he response to television and testing pulses of cables with nonuniform characteristic impedance (U eber das V erhalten von Kabeln mit W ellenw iderstandschw ankungen bei Fernseh- und M ess-im pulsen).
Arch, elekt. U ebertragung 7 (1953) nos 3 and 4, pp. 157— 162 and 191 — 198.
3) G. F u c h s : Reflections in a coaxial cable due to impedance irregularities.
Proc. Inst. Elect. Engrs, part IV 99 (1952) m onograph no 25 pp. 121 — 136 also published in: Cables et Transm ission 7 (1953) no 2, pp. 122— 141 (in French).
4) E. I. G r e e n, F. A. L e i b e and H. E. C u r t i s : T he proportioning of shielded circuits for minimum high-frequency attenuation. Bell Syst. tech.
J 15 (1936) no 2, pp. 248—283.
5) R. H o f f m a n n : T he technique of the local branches in the Germ an television netw ork. (Die Technik der O rtskabelleitungen im deutschen Fern- sehnetz) Fernm elde-Ingenieur 10 (1956) no 7, pp. 1—28.
6) K. R. W e n d t : Television D.C. Com ponent. R C A Review 9 (1948) no 1, pp. 85— 111.
7) E. C. C h e r r y and G. G. G o u r i e t: Some possibilities for compression of television signals by recoding. Proc. Inst. Electr. Engrs. part III 100
(1953) no. 63, pp. 9 — 18.
328
T he a u d ito ry .
November 1957 - Deel 22 - No 6 329
Som e audio problem s in modern telephone system s
by H. M o l* ) Summary
T h e p re se n t p a p e r gives a su rv ey o f th e audio problem s p e rta in in g to th e im provem ent o f th e transm ission q u a lity o f a telephone circuit. B esides th e im provem ent of elem ents th e stu d y o f th e fu n d a m e n ta l p roblem s of speech tu rn s ou t to be an im p o rta n t factor.
1. Introduction.
In general the av erag e rad io engineer lends a very unw illing e a r to audio transm ission problem s. P e rh a p s the follow ing, a d m ittedly v e ry b rie f survey w ill convince him of the existence of in terestin g problem s in this field, w o rth y of the atte n tio n of engineers.
O f course th e various subjects can n o t be p resen ted in the ro u n d : some subjects a re tre a te d m ore e la b o ra te ly because m ore is know n a b o u t them a t the m om ent. T his does n o t m ean th a t less tim e is o r should be d ev o ted to o th e r subjects th a t are d e a lt w ith in a few lines. In g e n eral the tre a tm e n t of th e p ro b lems is ad m itted ly stream lined to the nth degree b u t w e trie d to allev iate th a t deficiency b y giving a m odest num ber of re ferences to lite ra tu re .
2. The elements of a telephone-set.
In com m ercial telephony the classic device fo r transform ing sound into electrical signals still is, an d p ractically a lw a y s has been, the carb o n m icrophone. I t has been able to stan d its ground th a t long because it is an am plifier as w ell, providing a p o w er gain of some 30 dB . I t ad m itted ly h as a b a d re p u ta tion fo r d isto rtio n , in sta b ility and noise. C onsequently it is despised b y studio people w ho d iscard ed it as soon as th e y could invent ty p es of m icrophones b e tte r suited to th e ir purpose.
Since 19-15 the carb o n m icrophone has been stu d ied a t la b o rious length a t the T ransm ission L a b o ra to rie s w ith the aim of finding the lim iting fa c to rs of its perform ance. This stu d y w as n ecessitated by the re a lity th a t a fte r the end of W o rld W a r II G erm any ceased to be the m ain source of carb o n m icrophones fo r the N e th e rla n d s P T T . O n e sta rte d looking fo r an ap p ro
*) T ran sm issio n D e p a rtm e n t
330 H. Mol
p ria te su b stitu te fo r the alm o st classic Siem ens-m icrophone.A p a rt from some untim ely im provisations th is search tu rn e d out to be fruitless. I t w as in th a t situ atio n th a t the N e th e r
lan d s P T T u n d erto o k to compile a specification fo r the con
stru ctio n of a new ty p e of carb o n m icrophone th a t could be used th ro u g h o u t the N e th e rla n d s telephone n etw o rk . W e a t the la b o ra to rie s seized th e o p p o rtu n ity fo r in co rp o ratin g the la te s t th eo retical and p ra c tic a l findings in the design w hich also had to have norm alized o u te r dim ensions.
M o re o v e r th e m icrophone w as expected to function sa tis
fa c to rily in the m ultitude of different feeding S
3
Tstem s this co u n try could b o a st of a t th a t time.N eed less to sa y th a t a h o a rd of thought-provoking problem s w as th ro w n up, both of a p ra c tic a l an d a th e o re tic a l n a tu re . I t stan d s to reaso n th a t the ultim ate design tu rn e d o ut to be a com prom ise, fitted as it w ere b y le a st sq u ares to th e con
flicting requirem ents. In o rd e r to te s t our th e o re tic a l pro n o u n ce
m ents sev eral p ro to ty p e s w ere pro d u ced by the la b o ra to ry an d d e m o n strated to the in d u stry in o rd e r to facilita te the process of p u ttin g ideas into m ass-production. Though in gen eral P T T took the in itiativ e in th ese m a tte rs w e w ould do a grave injustice to the in d u stry , including th a t of the N e th e rla n d s, b y n o t m entioning and acknow ledging the p ain stak in g activities of the co n tractin g factories.
T he basic principles underlying the final design can be b riefly sum m arized as follow s. (
1
)The carb o n cham ber o f th e m icrophone is nothing b u t a mi
n iatu re co al-scuttle, the w alls ol w hich are in su lated except fo r th e tw o electro d es. I t is n ex t to a m iracle th a t th is collec
tion of loose co n tacts can be sta b le a t all. In a stab le m icro- ph one the carb o n g ranules rem ain in the sam e geom etric con
figuration th ro u g h o u t the d u ratio n of a telephone call. N ow , like a heap of sand, the g ra n u la r m ass h as the ten d en cy to assum e a sm aller volum e. In the m icrophone w e call this the phenom enon of packing. A m ong the m any fa c to rs th a t have a stak e in th e problem of packing d ry friction b etw een th e g ra nules p la y s an im p o rta n t role. D ry friction k eep s the packed g ranules in th e ir frozen condition, a g a in st th e re sto rin g forces furnished b y the polarizing d ire c t cu rren t. The influence of the feeding c u rre n t on the sta b ility can be eith e r d e tre m e n ta l or beneficial. W T en the g ranules are m echanically displaced along the stream lines of th e feeding c u rre n t the elec tro -sta tic forces
Some audio problems in modern telephone systems 331
b etw een th e gran u les w ill su p p o rt the packing action of d ry friction. If, on the o th er hand, th e granules are displaced p e rp en d icu larly to the stream lines, the electro -static forces w ill drive them b ack to th e ir original positions, in th a t w a y p ro v id ing an e la stic ity of e le c tro -sta tic origin. T his is the so called tra n sv e rse -c u rre n t principle. U n fo rtu n a te ly th e tra n sv e rse -c u r
re n t m icrophones suffer from a low output. O n the o th e r han d the m icrophones of obsolete design w ith flat electrodes th a t are exceedingly inviting to packing have a high output. The m odern com prom ise is the m icrophone w ith dom e-shaped electrodes, said electro d es being p a rts of spheres. H e re th e tra n sv e rse -c u rre n t principle is active only in certain p a rts of the carb o n cham ber.
The stabilized p a th w a y s as it w ere “keep up” ad jacen t stre a m lines th a t g u aran tee a higher o u tp u t b u t run the risk of packing.
F o r sta b ility it is essen tial to keep the to leran ces of the d is
tan ce b etw een the electro d es w ith in n a rro w lim its in m ass- production.
The freq u en cy resp o n se of the carb o n m icrophone is governed by the resonance of the diaphragm and its clam ping and b y the resonance of the carb o n cham ber. T he m echanical im pedance of the carb o n cham ber is non-linear and depends on the m ag
nitude of the displacem ent of the m oving electro d e. C o n seq u en tly the shape of the frequency resp o n se depends on the acoustic p ressu re of the sound field in w hich the m icrophone is te ste d . A lso packing m akes itse lf fe lt in th e freq u en cy response because packing increases the stiffness of the carb o n cham ber so th a t consequently th e lo w er end of the freq u en cy ran g e is a tte n u a te d .
Though, clearly , the freq u en cy response of the carb o n m icro
phone is a ra th e r vague affair, w e m ust n ev erth eless sm ooth out d istu rb in g m echanical resonances. T his can be done eith er b y intro d u cin g aco u stical o r m echanical lrictio n or, m ore ele
g an tly , b y adding ad d itio n al resonances, in o th e r w o rd s b y in
troducing m ore degrees of freedom . In this re sp e c t w e m eet the sam e ty p e of problem s in electro-dynam ic, electro-m agnetic, piezo-electric o r sem i-conductor m icrophones.
The harm onic d isto rtio n , even in a m odern carbon m icrophone can easily reach a value of some 20% . The se a t of th is d is
to rtio n is the n on-linear m echanical im pedance of the carbon- cham ber, as “ seen” from the m oving electro d e. In te re stin g enough, one can prove, bo th th eo retically an d experim entally, th a t the re la tio n b etw een re sista n c e -v aria tio n of the carb o n cham ber an d displacem ent of the m oving electro d e is su rp risin g ly lin ear. I t
332 H. Mol
is the no n -liaear carb o n im pedance th a t causes the non-linear re la tio n b etw een sound p ressu re an d resistan ce-v ariatio n . M any people pin the deficiences in intelligibility on the non-linear disto rtio n of the carb o n m icrophone. O u r prelim in ary m easurem ents, how ever, seem to indicate th a t the lim ited frequency ran g e is to blam e.
The only reaso n fo r discard in g th e carb o n m icrophone in fu tu re is th a t it w ill n o t be stab le on th e low line c u rre n ts electronic telephone exchanges w ill be ab le to furnish. In the U S A a sem i-conductor m icrophone (2) has been announced th a t req u ires only one te n th of the c u rre n t of a carb o n m icrophone.
A s it is a m o d u lato r it also provides am plification, ju s t like the carb o n m icrophone. I t is not, how ever, afflicted b
3
r packing.Since the invention of th e telephone in th e e arly seventies th e co nstruction of th e telephone receiv er h as n o t fu n d am en tally changed. I t still contains pole-pieces w ith coils, a p erm an en t m agnet an d a flat d iaphragm . The m ajor im provem ent w as the g ra d u a l red u ctio n in size of the p erm an en t m agnet. W h e re a s in the early days the m agnet w as used as a generously sized handle, quite often in m odern receiv ers the m agnet can h ard ly be found a t all. A b o u t 20 y e a rs ago it a p p e a re d th a t the fre quency resp o n se of th e receiv er could be m ade flat (so called equalized receiver) b y placing a h a rd surface v ery close behind th e d iaphragm , a tex tile-co v ered hole in this surface providing the n ecessary friction. Since sev eral y e a rs th is principle is in
c o rp o ra te d in th e new receiv ers th a t are introduced into the N e th e rla n d s telephone n e tw o rk . I t is in te re stin g to know , h o w ever, th a t said principle w as a lre a d y p re se n t in A d e r’s receiv e r (3), d atin g b ack to aro u n d 1880, though it w as n o t recog
nized as such a t th a t tim e.
Though the p re se n t ty p e of receiv er g u aran tees a good se r
vice th e re are sev eral reaso n s fo r replacing it by a d ifferent type in fu tu re. I t is difficult, fo r instance, to a d ju st an d keep sta b le the air-g ap b etw een th e d iaphragm an d th e pole pieces.
The diaphragm , being continuously exposed to the a ttra c tin g force of the p erm an en t m agnet, has the tendency to sag. A lso, th ere is th e d an g er of sa tu ra tin g the diaphragm an d m any va
ria n ts to the classic configuration have the sam e a im : lettin g the lines of force p ass the m em brane a t rig h t angles an d p re venting th e ir re tu rn th ro u g h the thin v ib ratin g p late. In the b alan ced m agnetic system s th ere is no c o n sta n t force of m ag
Some audio problems in modern telephone systems 333
netic origin on th e a rm a tu re , w hich is se p a ra te d from the cone- sh ap ed m em brane as such. In general, th e re is a lim it to screw ing up the m agnetic field because, a p a r t from sa tu ra tio n effects, the field acts as a tra n sfo rm e r ra tio m atching the m echanical system to the electric source. A s such it h as an optim um value (3).The co m p arativ ely high acoustic im pedance (as seen from the earpiece) of the p re se n t receiv er w ith its h ard , flat m em brane is felt as a d ra w b a c k because th e receiv er does n o t short- circuit the room noise w hich is produced b y a low -im pedance source, nam ely the air. M o reo v er the receiv er is a b a d ra d ia to r so th a t it cannot be used as a sm all lo u d sp eak er to rep lace the classic rin g e r w ith its gongs. The above-m entioned an d o th er problem s are still u n d er co nsideration fo r the tim e being.
3. The improvement of transmission quality
T hough re c e n tly developed ty p es of telephone receiv er such as the rin g -arm atu re (4) type an d the rocking arm a tu re ty p e give a su b sta n tia lly higher o u tp u t th a n the p re se n t type, th ere is a lim it to increasing the sensitivity of the receiver, fh e sam e argum ent holds fo r the m icrophone as w ill a p p e a r from the follow ing.
W h e n the to ta l a ir-to -a ir sensitivity of a telephone channel is too high th ere w ill be uncom fortable listening pro v id ed an autom atic volum e reg u latio n of some so rt ta k e s place w hich has m any technical consequences in the n etw o rk , W e think to have reach ed th a t com fortable lim it in th e P T T n etw o rk , considering th a t, in the com plete absence of noise, one can c a rry on a conv ersatio n via tw o m odern telephone sets even w ith an a t
ten u atio n of some 50 dB b etw een them . W h e n a w h ite noise of 0,5 V , as m easured w ith th e C C IT T -p so p h o m e te r a t the term inals of th e set, is p re se n t th is a tte n u a tio n reduces to some 35 dB.*) O n ly in noiseless n e tw o rk s a less sensitive m icrophone can be com pensated fo r b y an o v ersensitive receiver. W h e n th ere is noise p re se n t the m icrophone o u tp u t should be w ell above the noise level. S o-called sound p o w ered system s m ajr also cover a “ d ista n c e ” of 50 dB in the noiseless case, b u t u n d er the p revailing noise conditions in the p re se n t telephone system s th ey nev er have a chance.
In the m odern telephone se t th e m icrophone and th e receiv er
*) T hese figures m ay no t be re g a rd e d a s h a rd -a n d -fa st figures. T h ey m erely in d ic a te the o rd e r o f m ag nitude.
334 H. Mol
are coupled to the line by m eans of a balancing tran sfo rm er w hich reduces the so-called side-tone. The expression side-tone is technical ja rg o n fo r hearing one’s ow n voice coming from the receiv er w hich can be m ost u n p leasan t. The m ore the sen sitiv ity of bo th the m icrophone an d the telephone is screw ed up the m ore difficult it becom es to com bat side-tone. O n e of the m any solutions fo r th e balancing tra n sfo rm e r is the so-called O hne- sorge-system , am ong o th e r things ch aracterized by the fa c t th a t th e balancing resistan ce acts as a D C sh u n t acro ss th e m icrophone (w hich is beneficial to th e la tte r ’s sta b ility ) an d th e pro- p e rty th a t the receiv er is connected to a se p a ra te w inding on the tran sfo rm er. T he s e p a ra te w inding perm its the in sertio n of a tra n sito riz e d am plifier fo r th e h a rd of h earin g w ith o u t the need fo r an ad d itio n al tra n sfo rm e r, providing a gain of some 25 dB.
B efore the w a r th e O hnesorge-system w as used p ractically th ro u g h o u t th e N e th e rla n d s telephone n etw o rk .
I t w as m aintained in th e new telephone sets developed a fte r 1945 though the ra tio of th e w indings w as slig h tly changed in o rd e r to p erm it the tra n sfo rm e r to receive
100
Q m icrophones as w ell as 200 Q m icrophones. The 200 Li ty p e is n ecessitated by the 2 X 400 Q, 24 V feed ing coils of th e R o tte rd a m exchange.W h e n the a tte n u a tio n b etw een tw o telephone sets is reduced b y m eans of am plifiers, echo-problem s arise. In this co u n try the so-called 4 w ire-system is in g eneral use. A s the classic am plifiers are u n ila te ra l th ere are se p a ra te go- an d re tu rn p ath s.
The coupling of these p a th s to the su b scrib er’s lines is realized by b alance tran sfo rm e rs th a t also have the ta s k of p rev en tin g coupling b etw een the go- an d re tu rn p ath s. A s the balance conditions can n ev er be id eal th ere a lw ay s rem ains a certain am ount of coupling. C o n seq u en tly th e ta lk e r w ho sends speech w aves along the go-path h ears his ow n voice coming b ack v ia th e re tu rn -p a th in the form of an echo. T he higher its level an d the longer its tim e-delay the m ore d istu rb in g the ta lk e r’s echo w ill be. (5)
A d etailed d escrip tio n of the la b o ra to ry ’s engagem ent w ith the echo problem lies outside the lim ited scope of th is p a p e r.
W e shall confine ourselves to sta tin g the in terestin g fa c t th a t fo r this co u n try it is the im provem ent of th e echo conditions on in te rn a tio n a l lines th a t calls fo r expensive m easures in the n a tio n a l n etw o rk .
A s the im provem ent of tran sm issio n q u ality m arches on m ore
Some audio problems in modern telephone systems 335
problem s are posed to the transm ission engineer. F o r instance, th e possibilities of reducing the a tte n u a tio n in the p erip h eral ram ifications of the telephone n e tw o rk are c e rta in ly w o rth exploring. The telephone n etw o rk s of facto ries, the buildings of w hich are sp re a d over larg e a re a s, are n ev erth eless w ith o u t fu rth e r ado connected to the P T T -n e tw o rk via often a lre a d y long su b sc rib e r’s lines. I t is c ertain ly n ecessary to bring these n etw o rk s w ithin the scope of the g eneral im provem ent of tra n s m ission q u ality though a t the m om ent is n o t y e t quite clear w h a t w ill be the m ost econom ical m ethod. O n e m ight contem p la te loading*),
2
w ire am plifiers, negistors**) etc.In the long ru n no m odern transm ission la b o ra to ry can be blind to th e fu n d am en tal problem s of speech.
E sp ecially in (c arrier) system s w h ere the sam e channel is used fo r speech an d signalling th e signal receiv ers m ust be safe
g u ard ed ag a in st signal im itation b y speech. In th is re sp e c t again an d again one comes to the conclusion th a t our know ledge of the sta tistic a l p ro p erties of speech w av es is still fa r from m ature.
A lso several problem s of auto m atio n call fo r voice o p e ra te d devices.
Since the realizatio n of th e tra n sa tla n tic cable the a tten tio n of the w o rld is re-focussed on the vocoder problem (
6
). The vocoder aim s a t b an d w ith -red u ctio n (o r b e tte r: cap acity -red u ction) so th a t m ore th a n one telephone co nversation can be tra n s m itted over a " s tra ig h t” channel th a t norm ally carries only one conversation.
The co nstruction of a successful vocoder m ust, in our opinion, ro o t in a sound know ledge of the a rtic u la to ry an d a u d ito ry processes. W e m ust n ev er fo rg et th a t N a tu re , w ith its v a st experience in telecom m unication is our b e st te a c h e r and? th a t it has sound reaso n s fo r n o t applying certain techniques.
N eed less to say th a t the developm ent of a vocoder is only w o rth -w h ile fo r ap p licatio n to expensive circuits.
F o r the above m entioned reaso n s a sm all group a t the d r N e h e r L a b o ra to rie s is engaged in fu n d am en tal studies on speech.
Literature.
1) M o 1, d r. i r. H.: T heorie van de Koolmicrofoon (I) H et PTT-B edrijf, III (1950), no. 4, pp. 128— 134.
*) T h a t is in cre asin g the self-inductance o f the line b y in se rtin g coils.
**) T hese a re n eg ativ e im pedance am plifiers.
336 H. Mol
idem II, H et PTT -B edrijf, IV (1951), no. 1, pp. 3 4 -4 1 . idem III, H et PTT-B edrijf, IV (1952), no. 3, pp. 118 -1 2 4 . idem IV , H et PTT-B edrijf, V (1953), no. 2, pp. 8 4 -8 8 . idem V , H et PTT-B edrijf, V (1953) no. 3, pp. 1 1 2 -1 1 5 .
2) B u r n s , F. P.: Piezoresistive Sem iconductor M icrophone, JA SA 29 (1957) no. 2, pp. 248—253.
3) M o l , d r . i r. H.: Some theoretical pronouncem ents around A der’s receiver.
H et PT T -B edrijf V I (1955) no. 4, pp. 9 3 -9 6 .
4) M o t t , S. E. and M i n e r , R. C.: T h e Ring A rm ature T elephone Receiver, B STJ X X X (1951), pp. 1 1 0 -1 4 0 .
5) H u n 11 e y, H. R. : T ransm ission design of intertoll telephone trunks, B STJ 32 (1953) nr. 5, pp. 1019— 1036.
6) M o 1, d r. i r. H.: Some notes on the vocoder problem. H et PT T -B edrijf V II (1957) no. 4, pp. 1 1 4 -1 1 8 .
November 1957 - Deel 22 - No 6 337
N on-linear properties of carbon resistors
by C. E. M ulders *)
Summary
T he ap p lic atio n of the conv en tio n al m ethod of determ in in g the n o n -lin ear effects in c arb o n re sisto rs, as outlined in m an y te st specifications fo r these com ponents, e n co u n ters difficulties in case of good specim ens. An a lte r
nativ e m ethod is pro p o sed , b a se d on th e m easu rem en t o f the p ro d u ctio n o f h arm o n ics in the resisto r, w h en a p u re sinusoidal c u rre n t is p a ssin g thro u g h it. A d escrip tio n of the ex p erim en tal p ro c ed u re is given a n d some re su lts a re sh o w n . A com parison is m ade b e tw ee n bo th m ethods in som e cases w h e re e ith e r m ethod is ap plicable.
1. Introduction,
W ire -w o u n d re sisto rs g en erally obey O h m ’s law
V = i R , (1)
w h ere R, the resistan ce value, is a function of te m p eratu re.
E q u atio n (1) does n o t en tirely hold fo r carb o n resisto rs. A b e tte r ap proxim ation of the v o ltag e-cu rren t re la tio n fo r this type of re sisto r is given by
V = i R a ± a \ i " \ . (2)
(The n o tatio n + in this equation m ust be in te rp re te d in such a w a y th a t fo r positive i th e + sign m ust be used an d fo r negative i the — sign. In th is w a y V is a sym m etrical function of i, irresp ectiv e of the value of n, as in the case w ith carb o n resisto rs).
If w e define R, the resistan ce value, as the q u o tien t of V and i, (
2
) yields— = R = R a + a | z*-11 . (3) i
r) P h y sic a l d ep artm e n t.
338 C. E. Mulders
F o r carb o n resisto rs a | z’"-1
j is sm all com pared to R a an d negative. B o th R a a n d a are tem p e ra tu re d ependent, though the tem p eratu re dependence of the sm all term a [ z"-1
| w ill be gen erally neglected.F o r 7i —
2
, (3) becom esR — Ra + et I 2 [ R a -j- CL I V\
R a
o r R - R a = . (
4
)Ra
In th is case A-A is p ro p o rtio n al to the applied v o ltage an d a
“ voltage coefficient can be defined i.e. the p ercen tag e re s is t
ance v ariatio n p e r volt. So
voltage coefficient = y = ioo X A R R a X l V f or A R Y . R g - \ V \
IOO
C om paring (4) to (5) gives
a y . R l
IOO
(5)
(
6
) I t is common p ractice to give an allo w ab le u p p er lim it fo r a, as it re su lts from testin g p ro ced u res fo r carb o n resisto rs. I t w ill be show n, th a t the expo n en t in (3) is n o t n ecessarily 2, so th a t the “ voltage coefficient” concept can n o t a lw ay s be used.2. Conventional method for the determination of a or y.
A stra ig h tfo rw a rd m ethod to determ ine a o r y is to m easure R as a function of
2
o r F. B y su b stitu tin g the m easured values in (3) a an d y can be calculated.A difficulty arisin g w hen the m ethod is ap p lied is th a t the m easuring c u rre n t w ill cause the re sisto r to rise in tem p e ra tu re, w hich m eans th a t R a changes an d a w ro n g value of a j
2
V,_I | resu lts. A n obvious possib ility to overcom e th is difficulty is to m easure R so ra p id ly th a t no ap p reciab le rise in tem p eratu re w ill ta k e place. In e.g. the p ro ced u re as describ ed b y the R adio In d u s try C ouncil in the specifications R IC 112 an d 113 fo r “ resisto rs, fixed, com position” , such ra p id m easuring is pre-Non-linear properties of carbon resistors 339
scribed. “ The sam ples shall be d ried fo r 2 hours a t n o t less th a n 7 0°C. The voltage coefficient sh all be determ in ed b y m easuring the resistan ce value a t a voltage co rresponding to the norm al maximum ra tin g an d again a t
1
/IO th of th a t voltage.T he voltage sh all be ap p lied fo r n o t m ore th a n
1
second every10
seconds to avoid o v erh eatin g ” .F o r good carb o n resisto rs, how ever, w h ere a an d y are sm all, the said value of
1
second proved to be u n a c cep tab ly long. A n ex p erim en tal stu d y of the ra te of heating of re sisto rs of differe n t kind w as m ade an d the influence on resistan ce m easu re
m ents could be estim ated (see Section
8
).A descrip tio n of a p ro p o sed new m ethod fo r the determ in atio n of a and y w ill be given in the next Section.
3. Determination of a and y by measuring the harmonic production.
W h e n a pure sinusoidal c u rre n t t — tm stn cot p asses through a carb o n re sisto r, harm onics w ill be p re se n t in the voltage across the re sisto r, due to the non-linearity of (
2
) orV = R a im sin cot -Y a \ in sinn cot | . (
7
) The F o u rier expansion of th is equation isV = R a im sin cot 4- E x sin cot + E3 sin
3
cot + E s sin5
cot. + ___ (8
) O n ly uneven harm onics a p p e a r, due to the sym m etry of (2) an d (7).The m ost im p o rta n t fa c to r of (
8
) is E y A pplication of F o u rier analysis to (7) an d (8
) givesE3 sin
2 3
cot dcot — l a inm sin* cot sin3
cot dcot,so th a t
E 3 X n 2
n
a inm I sin* cot sin
3
cot dcot.O
(9)
The in teg ral in (9) w hich w ill be called / (n) has th e value340 C. E. Mulders
ƒ (n) = / sin" w t sin diot = —n — I
n +
3
n + I /rc, (10)fo r n >
so th a t (9) can be w ritte n in th e form
2
a £ , f ( n )^3 = — ot X
(2
, (11)w h ere
0
=2
f (n)/n .The follow ing ta b le gives values of ƒ (n) an d Q fo r a num ber of values of n
n / ( « ) Q
1.0 0 0
1.5 0.11 0.07 2.0 0.27 0.17 2.5 0.34 0.215 5.0 0.39 0.25 3.5 0.43 0.275
4. Experimental procedure.
a. A v e ry sim ple realizatio n of th e principle laid d ow n in Section 3 w ould be the follow ing.
A g e n e ra to r supplies a pure sinusoidal audio frequency cu r
re n t to the re sisto r u n d er te s t in series w ith a high-value w ire- w ound resisto r. The am plitude of the harm onic voltage across the re sisto r is m easured an d a and y can be calcu lated w ith the form ulae of S ection 3 an d 1.
A num erical exam ple, how ever, show s the difficulties encoun
te re d in th is p rocedure. T ake, fo r exam ple, a I w a tt jo o o f?
re sisto r fo r w hich n =
2
, so th a t the voltage coefficient definition can be applied. A n accep ted m axim um value fo r good carb o n re sisto rs fo r y is0.002 °/0
p e r volt, w hich, fo r th e re sisto r considered here, m eans th a t u n d er full load ( Ve/ f =
3
I-6
volt), according to (5) an d (
6
),A R =
0.63
Q an d a =20
Q . A1
.Non-linear properties of carbon resistors 341
T he am plitude of the fu n d am en tal c u rre n t a t full load follow s from the relatio n ----zi),X/? = W o r --- zj* X IOOO = I so th a t2 2
z«=
0.002
an d according to (1 1
)E3 =
20
X0.002
X0.17
=6.8
X io-3
V =6.8
m V ,the am plitude of the fu n d am en tal voltage a t th e sam e tim e being
31.6
/2
=45
volt.I t is clear th a t fo r the execution of the m easurem ent indi
cated here, the harm onic co n ten t of the g e n e ra to r m ust be con
sid erab ly less th an
6.8
m V , th e harm onic voltage g en erated in the resisto r. This m eans th a t, the fu n d am en tal voltage being 45 V , the harm onic co n ten t of th e g e n e ra to r m ust be less th an I.J X IO_2°/0. T his is, of course, difficult to realize. I t is also difficult to m easure the6
m V harm onic voltage in the presence of 45 V fundam ental voltage, so th a t the w av e a n a ly z e r fo r the m easurem ent of E3 w ill be com plicated.b. A n a lte rn a tiv e m ethod, in w hich b o th th e fu n d am en tal an d the harm onic voltage of the supply are balan ced in a
The re sisto r un d er in v esti
gation R x is in tro d u ced as one of th e fo u r arm s in a W h e a ts to n e bridge, to g eth er w ith th re e w ire-w ound re sis
to rs, one of w hich is a d ju st
able. A ll fo u r re sisto rs have ap p ro x im ately the sam e ohmic value. A udio-frequency voltage is supplied to the bridge in such a w a y th a t R x is lo ad ed to its ra te d w a tta g e . A w ave an aly zer th a t can be tun ed to th e fu n d am en tal as w ell as to the th ird harm onic voltage of the g e n e ra to r frequency, is con
n ected to th e bridge diagonal. B ridge equilibrium fo r th e fun
d am en tal voltage is estab lish ed b y m eans of the ad ju stab le re sisto r. In th is situ atio n bo th the fu n d am en tal an d the th ird harm onic frequency in so fa r as th e y are produced by the g e n e ra to r are n o t p re se n t in the bridge diagonal, so th a t m ea
su rem en t of the th ird harm onic v o ltage in th e diagonal now bridge, w ill be discussed now .
the m easu rem en t o f h arm onic p ro d uction in c arb o n resisto rs.
342 C. E. Mulders
gives an u n d istu rb ed indication of the harm onics produced in R x • L e t th e m easu red voltage of th e th ird harm onic be E 3. The relatio n b e tw e e n E3 an d the value of E3 as it a p p e a rs in (8
), can be calcu lated fo r a given bridge configuration. I t is, h ow ever, sim pler to determ ine th is re la tio n by calib ratio n . This can easily be done by in sertin g a given sm all voltage of an y freq u en cy in series w ith R x (E;„s in fig. 1) an d m easuring the v o ltage pro d u ced b y it in th e w ave a n a ly z e r in the bridge d ia gonal. T he m easured re la tio n b etw een th ese tw o voltages is the sam e as th a t b etw een E3 an d E 3, pro v id ed the bridge configura tio n is the sam e in b o th cases.
5. Some details of the method.
The m easurem ents can be c a rried out w ith sta n d a rd equip
m ent i.e. no excessive req u irem en ts are m ade on th e w av e a n a lyzer o r the audio freq u en cy o scillator. T he o scillato r m ust be able to supply the ra te d w a tta g e , w hich m eans th a t w hen e.g.
a 1 w a tt re sisto r is u n d e r te st, 4 w a tts m ust be supplied to th e bridge.
T he tra n sfo rm e r in th e brid g e d iagonal m ust have a ca re fully w ound sym m etrical p rim ary w inding, so th a t p o in ts A an d B (fig. 1) p re se n t th e sam e p a ra sitic im pedance to e a rth . A n e le c tro sta tic screen b e tw een p rim ary an d seco n d ary w inding m ust be p ro v id ed in o rd e r to p re v e n t false brid g e equilibrium . A sim ple m ethod to v erify w h e th e r these conditions are sa tis
fied is, to ta k e fo r R x a w ire-w o u n d re sisto r an d to m easure w h e th e r th e fu n d am en tal an d harm onic voltages in th e bridge d iagonal cancel o u t sim ultaneously.
6. Some measurements of non-linear behaviour of carbon resistors.
A num ber of re sisto rs of differen t values an d co nstructions w a s m easured according to the m ethod outlined in Sections 4 an d 5. T he ap plied audio-frequency w as 250 c/s, so th a t m ea
surem ents of harm onics w ere m ade a t 750 c/s. H arm onics w ere m easured a t a num ber of ap plied voltages up to the ra te d v oltage. Fig. 2a an d 2b give th e values of E3 as a function of th e p eak value of the ap p lied fu n d am en tal voltage, in a double logarithm ic p lo t. Fig. 2a gives values fo r crack ed -carb o n re sis
to rs,
2
b fo r com position-type resisto rs.Non-linear properties of carbon resistors 343
I t a p p e a rs from th e stra ig h t lines in figure 2a, th a t fo r crack ed -carb o n re sisto rs a sim ple exponential re la tio n as indicated b y (2) and (7) is valid. F o r com position-type resisto rs no such sim ple re la tio n holds, as is show n b y the curved lines in fig.
2
b.The value of the exponent n in (2) can be determ ined from the g rap h s by m eans of (
1 1
), from w hich w e derivelog E3 = n log im + log a +log Q . (12) n tu rn s o u t to be th e ta n g e n t of th e lines in fig.
2
a, assum ingP e a k value of th ird harm o n ic v o ltage p ro d u c e d b y th e p assag e o f a c u rre n t im sin (ot th ro u g h a re sisto r R a as
a function o f Ra •
F ig. 2a v alu es fo r c rac k e d -c a rb o n re sisto rs Fig. 2b values fo r com p o sitio n -ty p e re sisto rs.
344 C. E. Mulders
th a t a (and so log a) is in d ep en d en t of te m p e ra tu re. Since the points of the lines of fig.2
are m easu red a t d ifferent voltages, w hich m eans d ifferen t te m p e ra tu res of the re sisto r, log a in (12
) w ould not be a c o n stan t if a w ere a function of tem p eratu re.In Section 9 it w ill be show n b y se p a ra te m easurem ents th a t a is indeed only slig h tly d ep en d en t on te m p e ra tu re, so th a t log a can be ta k e n as a co n stan t.
7. Verification of the method.
F o r the com position-type resisto rs, w h ere the non-linear ef
fects are im p o rtan t, the conventional m ethod of Section 2, viz.
a d irect c u rre n t m ethod, gives reliab le re su lts, so th a t in these cases a com parison can be m ade w ith the new m ethod pro p o sed in the p re se n t article.
O n e of the re sisto rs of fig.
2
b, the1 200
Q one, w as chosen fo r th is p u rp o se an d its resistan ce fo r a num ber of d ifferent voltages in a W h e a t
stone bridge w as m easured b y m eans of d ire c t cu rren t.
The v o ltage w as ap p lied for the sh o rte st tim e n ecessary to m ake read in g possible.
Fig. 3 gives A R, the deviation of th e a c tu a l resistan ce from th a t m easu red w ith a v ery sm all voltage, as a function of the applied voltage. I t proves to be possible to re p re se n t the function by
A R = 7.0X io
-3
X V l6° (13) O n the o th e r hand, the m easurem ents of harm onic production of th is re sisto r as show n in fig. 2b enable us to determ ine A R . From the ta n g e n t of the slope of the function, it a p p e a rs th a t n is2
.35
, so th a t Q in (10) =0
.22
. F o r30
v o lt w e re a d from the g rap h E n =9
X IO-3
V an d R a being I140
Q, su b stitu tio n in (1 1
) yieldsE3 E3 X K _
9
X IQ~3
X1 140
"C X Q ~ V " X Q ~~ ~
30
" X0.22
0 _________ tO__________________ 20__________________30
► V
%
î n»AS'X N
n
1
Fig. 3.
A R as a fu n ctio n o f the v o ltah e acro ss a resisto r, d eterm in ed b y tw o m ethods, --- b y a D C m ethod --- b y h arm onic p roduction
m easurem ent.
a
N on-linear properties of carbon resistors S u b stitu tio n in (3) gives
345
R = a r 1 = a X j r
r:
9
X i o3
X1 140
" V ”30
“ X0.22 1140
”= 9 X IO 3 X II4 0 _ X y i .55 = 7 _g X IO -3 X J7'-55
3
o”'55
X0.22
The d o tte d line in fig. 3 re p re se n ts this function. I t w ill be seen th a t, alth o u g h the value of the exponent in (13) an d (14) is slightly d ifferent the o ver-all re p re se n ta tio n of the resu lts of b o th m ethods gives con sisten t values.
I t w ould be very in terestin g to com pare the re su lts of bo th m ethods fo r the crack ed -carb o n re sisto r in fig. 2a. The difficulty is obvious from the follow ing. The calculation of this Section ap p lied to th e
1200
Q re sisto r in fig.2
a w ould give a A R value a t full load of0.02
Q. In Section 2 it w as m entioned th a t the m easurem ent of such sm all resistan ce v ariatio n s is seriously ham pered b y the h eating of the re sisto r by the m easuring cu rre n t even fo r a v ery sh o rt m easuring tim e. The next Section w ill give some d etails ab o u t this heating-up effect.
8. Heating by the measuring current.
R x , the re sisto r to be te s t
ed, is again p a rt of a W h e a t
stone bridge, w hich is ap p ro x im ately b ro u g h t into equili
brium by m eans of the v a ri
able resistan ce R v . A t a mo
m ent t — O the voltage is a p plied to the bridge circuit and th e galv an o m eter is re a d as a function of tim e. From this the value of R x as a function of tim e a fte r the sw itching on of the c u rre n t can be calcu lated or determ ined b y calib ratio n . In fig. 5 the resistan ce is p lo tted as a function of tim e in such a w a y th a t <
5
R, th e difference of th e resistan ce value a t tim e t com pared w ith the in itial value, is given as a function of tim e. The th re e exam ples give th ree d ifferent ty p es of h e a ting effect. In fig. 5a, rep resen tin g the behav io u r of th e cracked- th e m easurem ent o f th e resistan ce
change d/\ due to the h e atin g effect of a c u rre n t.
346 C. E. Mulders
carb o n re sisto r of1200
Q in fig. 2a, ÔR can be ac c u ra tely d escribed b y an exponential function w ith one tim e-constant
<5 R = - i
8
(i - e ~ ‘u °) , w h ere t is ex p ressed in seconds.F o r the com position-type re sisto r in fig. 5b, w e find 6R = - i o (e-iho° - i) 20 ( e -th$
0
Fig. 5c rep re se n ts a re sisto r fo r w hich the resistan ce is no t a lin ear function of tem p e ra tu re so th a t an irre g u la r h eatin g curve resu lts.
From th e functions show n in fig. 5a an d 5b fo r w hich a sim ple m ath em atical expression can be found, an estim ation can be m ade of the resistan ce change imme
d ia te ly a fte r the sw itching on of the cu rren t. In the case of fig.
5a, 6R is
0.045
an d0.45
12 a fte r0.1
an d1
sec respectively. This value of O.045
@ com pares v e ry u n fav o u rab ly w ith the0.02
Q calcu lated fo r the non-linear effect of the sam e re sisto r a t full lo ad (see end of preceding Section). T his m eans th a t even a fte r so sh o rt a tim e as O. I sec the resistan ce change due to h eating is a lre a d y m ore th a n double the one to be expected from the non-linear effect.F ig. 5.
R e sistan c e ch an ce SR ifig. 4) as a function o f tim e fo r th ree resisto rs
o f different co n stru ctio n .
9. Temperature dependence of a.
10 20_________30
—► v
n
1
***■»*F ig. 6.
as a fu n ctio n o f F a t tw o tem p e ra tu res.
--- a t 70° C --- a t 90° C
I t w as m entioned in Section
6
th a t the calculations m ade are th ere v alid only if a is in d ep e n d en t of te m p e ra tu re. T h a t th e la tte r is indeed th e case can be p ro v ed by using a re sisto r w ith pronounced non
lin ear effects.
F igure