BSTJ 30: 1. January 1951: Theory of the Negative Impedance Converter. (Merrill, J.L., Jr.)

10.3 MB·English

‘Theory of the Negative Impedance Converter
By J. 1. MERRILL, J
(etait Bestel Yay 3.1350

staring ie ‘ike se ace tr

Lernapuenion

NEW type nf ielaore epmiar kina ashe Bf ea dang

reer met The lange dead nthe exchange en for anc
‘omic mears of proving treason gine o° about £09 in tee wire
Tap bres, deere ots less ta ye 2 ype ha me he
Sadan! igri, tay sins of mylyn ve erent he Bl
System. The diference i sat fade pesble by adileence in axerasing
Deneiple The TH reester expieys a eye o feedback emplier Ce asin
hie ea be od to have the prepertis fa negative mpecance converter.
Tie ye of per nse: open tat Ene nega
relincetnmverer hich fea vee for tranalonring peste pada

he negative naan
Negative inpecance se paatve elance ean have (20 components
reactance ad testance. The weactnce conposest cn be ether pasitie
lagative. Honescy forma impedence toe aegative she eisance comp
ert stole be aegtive at some fecusncy ia he reage fom. aero te
fuiy
heen of gave veiteas ovina awry 8 yee gy and ne

Iegining sas with she eunept of pine meee ean Tit
neg er fot te leva Ul fv ermal evn Srl ie

rend wtih bala ununtal propery we Saeed sien lh ing
tna ici en poutuce Une same ho of euctent a would fw eet
eaten fue prvige eit R were move rons this th,
Sppassily, she accion ton sei of 4 sye-temsing eemnt cul mee
tale an amount of resistance equal to R. Thus within ert fequency
lft this oer device cule bo eae as a negative resetnes equal
remegntae to
‘nezoay ay xian menace oosvEER »

In the cary dese of vocuums lube deveapment tae negative resistance
‘lee se considers to Bean inptant ne. Peasy the eenerative wae
un ie cet ascocisted ith dhe early rae rivers trl saest
ike sche the ofthe is: teat aol Lae Ua sac tbe ct
‘ulster abt 2g much Space Yo rgenerative mene lor pcg
gave vesiteee ait deveted to Cie Uncany aliry tn ary ore of te
snare eanversinl evi ly: amples, euler nls
Getcetats. Insite of the ntret fn the ee, il pa! ee was ale
ofthe nagalve resister tae

Nogitve rsitancevanant he competoly dsasocited fot reuscnce
Avacuunt cue viru arrange to devwnp negative resstace will present
reactance £3 lla ore Iequenrie, nnd the effect on. eh exter cuit
1 bse frequenaie wil De tof taking ame esteemed ag ot
subjecting fesctanee. At high al lw ieee the ie ly Peet
1 postive impedence. Corseruenlly, the Wem negtive impedence is used
lwmin tn esgnet the eee pred Iya twetmrina device mich bas
he popersy of negative resins at sun rey o fences,
ive resizance plus reactance aL her fans see ove impednce
aL atl other iequsoces

hue Nuoastse laeeoascr CosvrateR

Hretofore, nary seam tubs dicuts have been devs for converting
Drslive impedance inte oegative impedance. All Lown simple calle
mploing vac te for abeinng negetive imple, a atinesiske
Stora te cambin-tiom sie sench enn be mando ihe af vecute tubes
ovo ueylive denente found in mitre, have mich conan aad ca be
Ieated a the ame fope of arargument.Lastntay, thie typeof erage
"Rent ie feed ane and eye (raed each, Receatly. # ae
sethod of handing thes devin Yo hen leveloped hich bas the merit
fbsimpying somali fn tay aes This neo i bs mpon the
set ia! wisi tebe celts devged far couverting alive fsa
iu neative impedance cea be redued to an elecselly equivalent, our
frniual network consitng of © shinaton of puatve splay ee
bienis tagelicr wih ar seal naive impedance Comverse

"This ical eovverter, Fig.) rembles forts of tans: i has &
reso 9 tansfonsasin af J, can have fu terial a aonb of
Dinter tramiasn. Amwame lau siitve inoesanee Ze He canna
to terminal au and lz oem terminals and?, Fig: Ib} Tien
1 mest low fot Ce theory dese here than pve pede

5 Mae
oo mapyrns sverme reese yom, rosea 1951

Zc connected co teats {an 2, « nogasve rane Z.f8 xi be
‘eal ermine bad 4, Fi. 1.

‘Geange Crisonstete the these ate two types of some impadanoe
‘ohics he defnce asthe serie type ar the sun sype rept’. His
rie tne isthe reversed wage pe of atv ipedance —B2y ave
Tene ur VE; andi shuns ype ie she covered current yyw Za/—E
feivseat to Fy 1. This slit ever emdeiag tba mje
Thine 2 equal V7, and therelce nogetve imps (2) equals ether
yer er Fi Lhe ¥ ssl witage eewured across the rece and
Tis eucent fw teu i

? 7 2 1 7
& a 52 “ Pay
% a
oS _—
eel"

eis inportant so note thas & te ratio of trgsamation, if she Tar
10 hers both the magne tnd the angle © ate cheazig, bowen
Slowly wit fequeney Ths laws frome che fet tha, a il bestow,
“ction tery a) 1} eto na wltage aie the mngriite ad ase
feskt tan eienge wth freq

“Te rato uf rnaforation can be made te have a magne coy
spproachng unity, nd st sone Srseveney or Srnquencis che srg cape
tle sey TE en 1 he ses ype neg rapa soe ot te
th tid 2 Fig 16), wl he qual Zn, —P/, whee the volage F
Je severly {8D degree from the voltage shih wold anpene across ter
riled and 2 wore inpenance lene the pesil.veepedance Zy nr tre
Vilage to caveat ran tne omvestennl V/V. Tkewie, te shunt type
Tepe impedance es al terval and 4, Fig 1(0, wok he Za!
Toston tte ea the corent whies reverse ay 190 gre nn: the
current whith would do through he pif inpedanceZ,. Thos strnge
fact ip soles ulllsng © postive Impedance by ~T oes rt ye the
"ey oF yecaTeve mace Con ERIE a

some rele from a cteueviexpint ss Ailing » postive impedance by
A pastive inpodance etlplind by 1 fea sks ye gio
pele postive impedence ved yf Tear oye ol negalive
leper
‘A pnitil Ge, rel on acual) converter cicet aus Se retest yy
Rig. 16) A sacwurm tobe cnet contains positive fnpane east
Srime at thew wll show op in the equivalent circu on tae lead se
ofthe desl converter: ors will ow up onthe ghd seo the al
Converter Thi all he clan im ohe rsson ofthe Hl cick wie
Iellons. The npivalent tf ny practical aegis impedence eotveer
af hie type ea herpes Inte equivalent seit oF Lig 212 hc
hows C2 salve impecance cements auecisted sith thesaeima sabe ka

ila pty Ati eatiag
Se, 3 Sa
ate, ot
oy
Eide Sty ©
| 1 “hg
3 a

efor of ten aque neo (2 aa) aun eam ear side
ofc eal oomverter (0) hang transformation tet af 9:2
Mol Ue at du hs wr seme oa ines de
ovis ns of Wand auld the ssane relaonship exe forthe shunt a
then the eet of tes networks is canbe ete lor pr spation
sd 1g 16) ss eqaealns ca Fg. 1). Tinlad ig. 2 sae
fod Ye bave brea sepresnted by eqaialens T neo os shown apse
lyin Far 240). Network 7s canbe mailed ly al teatro to
te lethe side oF the dec converses, Eg. 20D) These serie arm
ofthe tn twarkscsael eachother asain Bg. 26) The nan arms
fav tints the hr scien arm cancel ening Fi 200).
ise eral yar Ye pelet in «aeticel cui sgn,
sat over she Eequensy’ ange of flea this sl be clsely pnts
by making ll intpnarces shunting the esl converte nage ns pes,
snd by canceling all tesstaces ia seven in Yy hye resintnee ace i
2 cae mun svemmecareantest wna, raseaRy 1ST

Asa physic concps the i of negusve pera yl to visual
fue becever ta type of imple supphss power 9 an exival siteuis
father then dist tals power is suopled ether hy theappliration of
teveos yoliage ora Teves tren, Taspite ofthe ly whi may
Ihe esoreyet in tenpting t vualize te feedback arton at takes
place inside a rpatvepedence ever if te eqsvsint eats known
Thc ie stabiiy can be deernined rend an Hs operation a5 a device
for pentving neste impeance becomes obvi
Spameere

Live any euler whose aut connerts ack his inp, the negative
impeaace copvertr ft ope cermin a Fa: acy ith tf and
tmelat. Stability ear he determined by woaventinnl frd-sek. theory
runt thee fea simpler eer for determining easily. Conse:
i thee! convey, Fag, Ab). Asset Za 22tskown on ig 12),
[Sten impedance vraosted fo terminals + aud 2. Consider the eel mesh
ome onthe left hen st oe deal converter Hy Ure comactin of Z
Iwas ad 2 Mens mgt imesianoe (EZ) ica leking into
Ivmivls {end 2 and nstivepedhres (2, lesen ok way"
them ‘The total Pees his mh &Z,— AZ. IE &Z should mpl
Zein the toa reac woul ere al vgs insried in ries
‘eit this mesh woul al for inte cree, 2 Stastion ebviniey my
[be Thue it bonnes evideus thie €Zy nol nt qual Ze, at's the
Sane hing the rin (qo nok eral 1/0 the este 3 bn be
Sable, Purtrsrnc, sea be shorn that fora ea comer the rc
zp/ds conaits the charles of Ge Food (ace [sof Zhe am
Diller in the converte, In vow of this fr, it wight be expected that
nits ele for stay a eta arpler could pares as
falls: > ete ei fae io mets impedance eae as
tf ibe ratio Rl 2 ere regan roe (rm ere ity mv en
tle the pol 2/9

re ane general ni for tity cen be arsived at ay connecting 1
inmpedance Zs totermnls Sand of Tig fe) nl by consering he iret
the formed hy (Za Py He sl be ote p ts ease bt 2,78
Calle for ow of carmen IND grees out of er Tern th chic wou
Mow Dvough Zc/# This men that whee the plnse angle of Zeal
thos of Zy the tonite uf Za must be ener thas that of Z, whi is
usher way of sig hub at this phase ele “ie magnitude of BZ:
be se ca unity

SHIM Repecat Ths B.S2.2 Jay
‘oan oe MRAM nersonnes cn ne 9s

Hor a practical exgineeing sonia Ceres ¢ sbupe eiteron for
ling sabi. It can bested olla: Tle et negative impedance
Converter will fe ancnsitonally stable provided shat te meat
e221 ean than writy at ag lssqueny wher the ata 08 is nto fe

Those sine covltins for steiiy apply to any practical (la, al ar
sri) converter cits, Hig. Gd). Hamever, Zed be taken he in
Dace sea loki ain the ato frum the positon of the Heal
fomvecte: C, ata Zy mst oe fkeoa thpw ern loking ito the
netwnrk 82 rom the ida! eamvertr C. la vite wumlsy the eect of Ny
ust Ie inched 2, apd the elo of mast be inl fn

Neos buensor Cosvutras Cram

Nevotve impedence can ns prs oy contteting the snipes of ax
ampler back in sres ori shat with te opt in he ight pase tle
tionship. "Thi typeof creat can he onsbered ae x nogctive ‘pene
sever smiles € Fig. 160} where reat tension —€ fo the
fer — yan which gy squewnt fenton the wags amples
tion of Ui ampli The dindvantage of tasers rai of ts kine
Js that it changes randy with vith fn tube coassats nba ey
apply velage. Such eizets prea slaliigy posi, Ove stan to
this problen Fas tre deserted by E.L Ginoton' He nga nei ot
ine ample gais ylang the semper ill wih rate feed.
Tack ats edaced variation fry Note thas fy Ses qual to, thea
Tetecumes egal t9 1
“There i ances uate wong mative Soda ty laine ict
for prising tive impedgnce. Ths ethos wae used in UF sia
‘adil be oer in deta in connection with st. Resta, hese nega
te fenack Ssranged togeier with pole Tole vo prduce a ai
formation ratio for Le ie converter ofthe fom = Ge Tae |b.
‘The symbol op seyecena = vole mila urtbertces a ep It
sprites unity aad iy very mer ages tha ey —E appr hes
1g ale and ie Eltivaly depen of visions in tbe eortants

saul latte app voltage,
Tz onler tn irate he coat ies of agacve inane
onset a ices conse cia cried Io Maras Latour abst

tie year 190, Fig So) Higure Sl) i © senate representation of Pi
Sin inthe manne rginte HU, Coes, Wil elerenes to Fi, he
ose of cpr i asasme sh tht, athe fst fe ne cuaest

1. fom ia che Wnetinn indi the teat sl Tow the ietion

EL Ginn Sid Nope Impose Bla Jl 8
Ok rm nets wsenec TeemacAL yuCHNy UAH 198

sown and the voltages Vs and adv wl lave the pstres shown, For
the moment will be astoved shat the fut ixpedasee of anpliner A
ify high an assumption whic wil be mood ner to goee wth

presen tupedaace,R, vests
i ar 2 eptoent Lae lege

the te resis eof Se xp
Jwoduced in he pate Set of she output cube of amphies 8, ee tube

‘Too! Fi, Sa) by the wetage doy HZ acrobat cathe of
Tr Vig Ma). hes equation foe Fig) Mo) can be te 6 allows:

Vin Bat 70
0 = Git eze

The con becomes

Vall, +7

oF
TTR FE e BO

sapedance scan looking io vein 1 anc 2 can be weil

Veo Be yr (1 8 eo
ete ta (tnt) ee
‘nipoxy oF Secanrvr DerzDaNee cove 95

‘THs the inprince Ze cquss the pease Zin pale with Ry
Which combition sin Saes with mpinge. Ze aati by
T= Ta2y (Re Zl Ancguivaleat cee for Ze tuetinted in Fig 6

Nest anon vt Z, not shown on Fig. (a coneaed b tknmal
ant 2 of Fir Sb and that Zp is ueioved irom across terial 3nd
ae aes uations cea be witen a lls
-Mr2an ~2

Zit Wy = Zi

w
‘The rorene 2, ean be writin:

2 PR a
Bt 11a, = 2-7
“The impedance ooking into tranny 4a §, 5g (8b, with the changes

Usted above ies

in a, (8)

Bars

pay

ve
tan

can)

Hany, i he certo Fig 800) 5 edesnm a fo termina aebnenk
show in Fig} wlh ated taepresert te ing ipa aro
fer A hoequivalest cai of Ih metork an be repose od ly Fg 16),
ne equivalent crew sagists af two pstive inane neo, oe
saves sie of ap Wel corverer. Tle aL of arson of thie Heck
fonveriee it of he form (9, USL Leaking into terminals Las 2,
Tig. 4), a serer ype negative impedance will be see hoking ito
tecniale Sal 'vsht type negative impel le wer The pro
‘hat these impecances are negate and of the revenge vollae or revered
arent type has been eataahel hy HW. Duley, FH. Graham snd
RC. Maths for sinter iets ll rot be tle ey al ng the
fx could be dered ssl fru enuntione 1. 2) 13) aa Hh. The
Irie of ohis disuse 40 ustate De simple ith which a
{gubalen sie can be derive, end to pin wt he vale of the concept
of Le ie sectivesnplane rameter,

All known sini ehish en be at gave ine wonerter
ie the een af the 21 type repeats La this he ong ihe ah
Fee fe ected ack tr te input shraigh mide ts 9 erage
relazed te €& a lybeid coi. Negative fnflck aed postive feb con
Itrvclped ees this eal between the amplier out i ls ie
int. Tis device was vse! cx negative impede caer yy Cosa
in hie rir type open,
96 um ners vanase maexsuea,yomevat, rasuany 1981

‘These is arcthe: ty of nsgative eepedance cenveter eimai which
huuid not be conivad sith the ervertr creatszeotionst hereon.
"This ype was disney Chares Tel inthe March 1927 fae of Che

Siwesal EB, pager 373 $76, the Barat souveter consis af 3 T
Tetwork of equal ratanees, one of lien negative. To conseve sich a
Converter Unie ust be avilable 4 rgyetse rsstance ween. Over &
cz op saver ewanater eaNvEREE o

finite tequeney and this native rsitnce cua be pout bya comseier
sireut ee 3 a of Fig. neers, nists Balt comes
in tne, a Gonveser within asonverie,

‘Tae Necanwe eorpaver Locus

Belore the BI sype of convener is dsr i wll ne well 1 con
sider, a gener, the mposinace chatscteretic wis can Iw proved. by
4 unptive plane coneertes The ape af the inpedesce sharers
over she ‘ne teney mgr, r°> to inky, looking fe erly Tso 2
for ino torairal $ amt of «negative dmpocantecenveces wl be valle
the sepa inspire asi Tt convene to ple tices he polar
four wh rngiesy #4 "sensing? parameter ‘Te leus eae deri
for any croul by means ofthe theory eutied by K. i. Van Wo nen for
Pesitive two tera nyu?

Tov scl cumiler he eaerterof Fig 4, Aseuve chat an geass
sch ae that shown in Fig Sa) in conrected to terminals Sand of F's. 4
suse 2; of Tig 4 ica taylan al hat oth &, ac Zi ace ee

ners. Now Fg. Sle} remrals «swt femiml aeterk rate pf &
steve evanted by ah indue:sace. The ‘eke of tai poaive mapeance
Doe on the Rand j¥ plane over Che Feuery ming irom pt ne
fine shova ak Hg. Sth). MU ame Faqueney Tie imple ena ot
ied recency ote pevanre eR Teta the vetwock of Fig Si © eae
Pactaice isa’, ta presen Z) of Vig 4. te inpedaare of the net
"vk 3 ore, Fg Se blows te ce ot Hig (@) A ae Bscuey
the pedance ew, at the secman. ieqerey the impodene
av st inte fluency the Sipelane feo again tae impede
Df hie etrork, Fig. Se), ore vse Uewagh ariel negate rape
aise converte, Hg. He, Roving aio of Sistas oo EE nb
fr Ie mamen, # os aasuved 20 be @ nnerie gee the ene frequen
rigs, the impesinee evs con be represented by Fig. st OF vous,
vl cloays lave on anpe =I high atl lw fequescies bug, 22 ak
‘pptssnaton, at kal, ean Tesssumel that over nos of te fequeney
igen inthe impedance digeame of Figs sf) and Tig 30h) pe
prove a romeric the cicit aaiguraion fig. (gh erate by
leingvessteace Ky in sree wl Fy ie) the impestince los lake
Hike thao Hig 0h, Theis sere ype restive inesanen al snvatee
"ye ran sen ove a lnrge postion 2 the fcjueney nu bei
teerisals Land 20! Fg dwt the smotetaal elyuck 9! Fg Si son
nested Uo tena Sane