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RESEARCH DEP ART.MENT THE nC:ENERAL RADIO" mH'lTANCE METER Inves tig"a tion by: P.Knight. J.W.H.O'Clarey. Report written by: P.Knight. G.DeMontea the Report No .G.05l Serial No.1952/23 (W.Proctor Wilson).

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RESEARCH DEP ART.MENT

THE nC:ENERAL RADIO" mH'lTANCE METER

Inves tig"a tion by:

P.Knight. J.W.H.O'Clarey.

Report written by:

P.Knight. G.DeMontea the

Report No .G.05l Serial No.1952/23

(W.Proctor Wilson).

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Research Department Co.NFIDENTIAL .

REPo.RT NO. G051 SERIAL NO.. 1952/23

December, 1952 .

Fig .. Nos. 1 - 8

TEE "GENERJ.L RLDIO" All:1ITTlil'l'CE },lETER

Summary

Anew' type of admittanc'e-measuring.device has been developed· . by the General Radio Company of .America. Al though opera tea as a: bridge, it may be used at ultra-high frequencies, at which impedance; or admittance measurement is normally restricted, to slotted-line techniques. The report describes performance tests, and discusses possible sources of error. The admittance meter forms part of a range of equipment for u.h.f. measurements; other items are described briefly.

1. Introduction

The General Radio u.h,f.admi ttance meter~ forms part of a range of equipment developed: by the General Radio Company of' . America for u.h.f. measuremer~ts. Although the principal object of the investigation WaS to assess the usefulness of the ac1mi ttance meter itself, some observations',are made on the associated equipment.

The normai frequency-range clalied for. the acJcl. ttance meter is 66 - 10.0.0. Mc/s, bridging' thegapbetvveen v.hS. bridges and u.h.f. standing-vvave indicators. . The meter is essentially a. direct-reading bridge, readings being taken by adjusting for a null, and it is. ~ therefore more convenient to use than a standing-wave indicator. 'It does,- however, share one dlsadv:antagewi th standing-wave fudicators: the measured aaini ttanoe is ref.erred to an inaccesible paint ina' transmission~lirie' forpling part of the ·instl:'UII1ent. Since this tran~mission-line has a characteristic impedance of 50. ohms, whereas 70. om cables are more usual in this coUntry, an additional application of the circle diagram is necessary' ill order to interpret the re suI ts" . . .

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\ Conductnnces, nnd susceptnnces 'between 0 nnd 400 mill:imhos can be measured. The makers cla:im~'the following accuracy for both conductnnce and susceptance:-

, 0 - 20 mnhos : -

20 - 4-00 rmnho s :-

;±(5% + 0.2 mmhos)

.±:5/M%, where M is the scale­multiplying factor

It ~vill be observed that the accuracy is greatest when measuring 20 nf2hos, i.e. 50 ohms.

2. DeBcription of thB equipment

2.1 Ire adrnit"tancenetcr

A schemn.tic (liagremof the aClmittance neter(reproduc.edfrQm the makerl:t instructions) is shown ~n Fig.l. It· ,consists essep.tially of ' three transmission lines haVing l;1. cOr:J!l1on junction to which the" generator is connected. These lines ar.e tel'r1.iriated respectively ,by a stanclard conductance, a stanctard susceptDJ1.ce, &'1d the Unknovl.n admittnnce, The current entering each branch is sampled by a loop whose coupling cnn be varied, and the three loops are' connected to a detector, so that an:. .... ll is obtl1ined ,when the sum of the vol tages induced in them is zero.' Now the cUl:'Tents in the three branches are proportional' to the a&n:i. tta:nceu teruina ting them. Thus the .. ~own a&l1ittance nay be deternined from the relation.

l~ (Gx +. j~) + ~GS + jMBBs ='0'

where ]fly, ~,~ and,~ are themutual:impedonces between~lle loops, and the 1iraltsmission, lines to which they are c9ul?led, G~. + jJ?x th. e ' unkno'Wn admittance '(referred' to the junction), 811(t ~~d ~BS the, stanc1n.rd conductance and susceptance, respectively •

. The control that determines ~ is calibrated .in terms of . cand'Ll:ctnncefrom 0 to 20mmhos, whiletl1e susceptpnce contrQl detennining M . is calibrate cl from ..,.20 to +20 mmhoso ',The rema,ining con~ol, vrhic~ deterr.rl.nes :lf

X; is calibrated in terr.is o~ a, scale­

multiplying factcr,by whic;:l the. readings of the other controls. are multiplied. Factors of 1, 2,5, 10 and 20 nre available.

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The three loops are shielded from the lines by Faraday screens, thereby eliminating capacitatiye coupling. Although they are connected to the detector in parallel rather than in series, a null is obtainec1 when the sum of the induced voltages is zero, since the self-impedances of the loops are equal. The standard conductance is b.or.1inally equal to the characteristic a&ni ttance of the lines, , and the magnitude of the st,~"I.!'d susceptance is set at each frequency to be' equal to the same quantity.. .'l.t low frequencies the standard susceptance is a 11./8 short-circuited line, bu,t above 500 ],ro!s a 3'A./8 line has to ~e used.

The standard: susceptanqe stubs supplied with the meter are calibrated in tenns of frequency, but it is advisable to check their cali"bration. According to the maker's instructions, this'is accomplished by first turning all three loops to the positions Qf minimum coupling. The conduc~ance and susceptance loops are then moV'ed in turn to the, 20 mmho po si tion (maximum. coupling) and the detector outputs compared. When these are equal the l;!tandard susceptarce is correctly adjusted. Errors due to the use of the meJcerl s calibration are u~ually small.,

It will be seen that the calibration of the stand.e.rd susceptance' depends on the accuracy of the~ standard conductance. The effect of any mism!),tch of the lat-GEir is, discussed in Section 3 and in l~ppendix li.

2.2 ~sociated eguipnlent

A feature of the adinfttance ,meter and its associated equipment is a novel type of connector ,which eliminates the necessity for 'male­female adaptors. These'plugs appear to be well designed electrically, but require care in use to avoid breakage,'

Slotted line (Type 874...tB) :

A'slotted line of theconyentional pattern forms part of the equipment. Its le~gth is' 55 Ofif' and it is therefore intended, fOl:­frequencies abovE; 300 MC/s. The probe unit can be connected direct to a receiver or maybe used as' a tuned crystal-detector. The line is somewhat lacking iri mecn.'1.nical rigidity and unless' considerable care is taken, insertion of,thebrysta;I,. tuning unit may temporarily distort the outer conductor. ,', Variation of the probe coupling with posi tion along the line 'Iiv'as. inves tiga tea at 900 Mc/s" using Sl, ' penetration of approximately 30%,.: ,The extreme values o£.the coupling differed by 37'0. ' ,

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> .~he line giyes satisfactory results when used with a receiver, but, when the crystal.c.etectol~ incorpo!ated :in the probe unit is

,u,sea., the apparent la"v of the 9rystal 'Varies considerably with the tu:p.:ing - a CQITlJ1lon fault in. lines having this type of detector. But the setting of the probe tuning con~rol was found to depend on the mwcim'l'ttrl output current obta:inedo As a result the detector cal:i,brat:ion. vaJ:'ied .D:Cco~ingtothe strength of the signal at the

,,'time of tuning. Vari.ati:ons in crystal law dne to this effect . Viere elimina ta.d, while;st:i.ll maintaip.i...'"lg adequate sensi ti vi ty, by

shunting tb'.3· probe with a 680 ,.ohm ;r-esistor" . .

.A micrometer is proVided to enable large standing wave ratios to be ·mec.sured 1:Y' th!? Itwidth of· the minimum" method. But since greht aC'curacy cannot' normally be" obtained, or is indeed seldom. required,ft)r widely mismatched :impedances, the usefulness of this 'refinement wot~d appear to be restricted to approximate measurements of cable 1osso

The 'slotted line Vias . used to measure a range of ac1m:i ttances which were also measured on the admi ttnnce meter. .An assessment of the accuracy of the latter instru.'!I.entwas then based on the assumption that its errors would not be greatarthan the discrepancies b(;j'b.veen ~he two measurements., ' It follows,. cQrrversely, that the accuracy of the s 10 ttC'd. line mus t lie within the same limits. The res1.Jlts of the co'dparisons. arediscusseq. in Section 5.

Fijced attenuators (Tyges 'S74-GG uno. 874-GF )

These are two 5O-obm coaxial 1t-type'littenuators with transmission lossed of'l.O and 20 db,~espectively. Some tests vvere Ja made on the :10 db at~e~1.Uator and it was found that its characteristic .. ' impedance and loss at, D.O. were 53 ohms and 9.6 db respectively. At 500 :Mc/sthe qhqI,acteristiC;imped,ance' YIaS found to be 50.5 ohms. A shunt capacitance of b.75I.l.!J.F vvas81so noted at theattenuator input; 'part of this maybe introduced 1:(y the connector ..

, .' ,." ... ". ". ". ."..'

Adjustable' ,~tte~lu~t~r '(t;rpe'874-GA) .. '

Th:l.sis a piston attenuator uslngth~ ,TE mode, excited 1:(y a short transmission 1:ine having a connector at~ach end. For most purposes this ane is terminated in a n.atched load. The attenuator has a calibrated range of 1:,:0 db; the minimum insertion loss at 1000 11c/s is sto.ted to b~ 33 (I.b.

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Mixer rectifier (.£Iype 874~,ffi)2

This is a frequency convertor employing a crystal detector; it is useful fer measureBents at frequencies for which no receiver is available.. Its frequency range is 50 to 3000 MC/s, with an output frequency not exceeding 40 Mc/s.. .Arl external oscillator is required. '

Telescopic line (We 874--LA)

This is a sliding line in two sections, having a 2:1 extension. Its characteristic impedance is 49 ohms when closed and 56.5 ohms when fully extencled... The line beconesnori-uniform 1i,hen it is partially extended, and it is not, therefore, sui table for accura:te work ..

Adjus table stubs (Types 874-D20 and 874-D5Q)

These are 50 ohm transmission lines, 20 cm and 50 cm in length respectively, 'Vdth a sliding short-circuit. These are uncalibrated but similar to the calibrated stubs used as standard susceptances •.

UaH.F. anCi. V.H.F" oscillators (Types 1208A and 1209A)3

. These are trio de oscillators coveripg the ranges 65 to 500 U.c/s and 250 to 920 Uc/s respectively; they are used in conJU!'ction with Type 1205A power-suppl:y' u:rii ts. A' simple variable coupling toa .. coaxial-line output is proVided" :The maximum output power is be.tween 100 and 500 milliwatts, wtlich is more thc..'Ul sufficient for operating the afuni ttance metel' or the slotted line, and the OSCillator;:; are . ideally suited to these' uses;, Either moy also be used as ,'8. 109.al oscillator when the mixer rectifier is employed.

3. §..ource s of error

The tests per~ormed on the admittance meter are described in detail in the next section.< Before' discussing them it' is of intere.stto consider the sources of error inherent in the design.

With any type of impeda:..lc.e-ffieas~ing aquipment, mismatch at cable connectors is always a major source of error. According to an approximate theoretical e~timate, the connectors used vdth this equipment are believed to introduce an excess shunt capacitance

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of the order of 0.25 ~~F. This would result in a reflection coefficient of 0,,02 at 500 lie/s.. It should, hoyvever, be noted that the standard conductance, which is a separate unit, is connected tf) the meter in the same manner as the unknown admittance .. Thus when matched a~~ttancesare measured, errors caused qy the two conneQtors will tend{;o cancel one another ..

In the operation of the meter it i~ assumed that a cqmnon voltage is applied to. the th1.~ee 'transmission lines, and that each loop samples the current in one of the lines at the jUnction point. But in order to ,ensur'e that each loop couples to one line only, and that there is no interaction between loops; each loop must be displaced from the junction.. Error will, be caused by the fact thl3.t the voltages in the three lines at the points where the currents are 'qomparea'dll ,differ :tromone ru1o-l;her~aridfrom the vol tageat the' 'jU:r;lCt:tono' The cause of thisvolt~ge difference, and hence of the er-.t:'or, is the' f'initf'1inductance o;f':,the 'transmission line between each coupling loop and the: juncti .. m"

It is shovVIl in Appoxl,dix,I that, tq, t,he first order of small quantities, the true admi ttance"G,+ ,jBand ,the measured ,a.dmittance Gt -+ jBt are related by the equation:-

,0;:= (j"

B = b' + ai..Yo - G' ) . . .' :

(1) ',"

where Y is the cbarac'teristic aCbni tta.nce of';the transmission-line ,Md CL iQ the SP1.cing in, ram.iUis bet\Ve~n each loop>and 'the junction.

, "

, Fig. 2, a cross-sec cbn'of' the jW1ction, shows 'that the:makers hiive taken steps to reclucethe inductance between each coupling loop and the junction by reducing; thediarheter of the outercondu'ctor. In order to take account of non-uniform Ilnes CL should be redefined as CL = wL1 , wherew is thea~lar frequency and L is ,the total series indBctance (in Henrys)- between each, lo6p arid the junction. From Fig.2, L is found to be 1.1 x 10-9 Henrys, which equals the inductance of 0 0 7 cm of 50 ohn transmission line. This calculation ignores the additional inductance cansed by, the ·slots.fDrmihgthe. Faraday screens.

It should be noted tha.t' eqUc'ition (l}sh()wsth~ error to be zero when the cdr..1uctance equals the charac'lieri'sticaatli ttance 'of'the ],.ine.. Under these con~ tions, the effects of the inductances

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in the T conductance t and 'f:1.IDlmcwnl branches cancel out. The effect of the in~uctance in'the1susceptance' branch is automatically corrected for in the method of calibrating the stub. The effective value of. a, as determined from the test described in Section 4.1, was f01.IDd to correspond to the length in radians of 0.93 cm of line. Application of the correction qy substituting in equation (1) gives the admittanGe at the j1.IDction. ThecOITected susceptance measured wheI1. the meter terminals are short-circuited enables the equivalent length of 50 ohm line betvreenthe plug and the junction to be calculated. Thus the measured admittance may be referred to the meter terminals. ., .

EITors are also caused by mismatch of the standard conductance • . It is shown in Appendix 11 that if the admittance of the standard

cunductancc, referred to the junction, is Y.j. ~G + j$, then the, resul ting conductance error is GII&G/Y

Q and ~he susceptance. eITor is

(G11 5B + Btt~G ~ where. G" and BtI are the measured conductance and , susceptance res pecti vely. The svm of the standard conduc tance was measured at a number of frequencies on the siottedline and was found to be better than 0.94 a.t frequencies below 900 MC/s. Thus a conductance eITor of 6% is possible, and susceptance errors.of -tthe same order of magni tude(U'e to be expected. It is, however, possible that part of ithe mismatch is associated 'with the connector, in which case the error vvill be smaller for nearly matched 108,ds, for the reason discussed above.

4. Performo.nce tests

4.1 Ueasurement o~,pur'e suscepta:nces

The apparent aClmitt:ance of a variable~leI1.gth shtb was measured, as a f1.IDction of the length, at frequencies of 200, 500 and 900 MC/s. The apparent length was ca,lculatedfrom the admittance and compared with the physico'l length, measured from an. arbi h'ary fixed. point. The re su 1 ts are s hovVIl in the solid curves or F~gs. 3 - 5.

If no errors 'Were present the curves would' be straight lines parallel to the axis, but displaced fram it because the physical length contains an arbitrary constant. Assuming the oscillation to be due mainly to the displacement of the loops from the junction, its peak-to -peak amplitude itvill be equal to the displacement. This Was found ,to be 0.90 ems at,.500 MC/s and 0.96 CrliS at' 900 MC/s; 'the '200 MC/s

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test d.id not proa.uce a canplete osci11ationo Taking the mean value as 0.93 cms, 0. (defined in Section 3) is given. by 2?tx 0 .. 93~ = 508;\ raclians,. By substituting this value in eq1..l.ation (1), the readings . at all Jvlr.:ed frequencies were correoted, giving the broken curves in Figs o3 - 5.. It vd11 be seen that the amplitude of the oscillation has been considerably rec.uced.The fact that the correction :is effective at three widely d~ffering frequencies justifies the original as~umption chat the 0;Jcillat10n of the CUTVE-S was caused by disp1ac8r.lent of the loops from the junction~

4-02 Measu.rement of matched adrni ttance _.~_ _;:";;"=..-,;0.

A. reasonably weJ.1-raatohed ternination was measurod both on the slotted line and on the admittDnce meter at a number of frequencies s

In order to compare the slotted line measuroments vvi th the a&ni tta..'1.CO moter readings, the forn~r were referred to a point on the line whose posi'bion was equivalent to that of the junction" (The apparent length of uniform line be~veen the junction and the cable connector had been previous::"ydeducecl from corrected susceptance measurements made w:i.. th the connector terminatec1 by a short-circuit).

The. results are compared in Fig.,6., It should "e noted that the mismatoh introduced by the connector is cor:unon to both measUl .... ements. The correction for the clisp1acement of the loops from the junctior. is. small be,cause the .. condllctar,c8clo~s not depart greatly fran the characteristic acJrn.i tta11ce of the system.. ':tt vdll be see"1. that the meter measurements ob';:ained at 500 MC/s ~th A/8 ahd. 3A/8 standard suscept&"1.ces are not in exact agreement.

4-03 Measurement of ...£lisma tohed a&n:i,ttances

The previous test was repeated at two frequencies with a mismatohecl terni.7lation which gave a stand:ing-wave ratio of about 0.3. To enable a full range of aa.m1ttancesto be measured, the termination Was connected to .themeasuring equipment vd th the telescopic line • Owing to .the imperfections Of t1">is line it was not expected that the admittances measured 't:i th various extensIons would lie on a circle when. plottecl. However, it "vi11 be seen from Figs. 7' and 8 that reasonably good approx:imationswere obtained. At 500 MC/s the admittance meter measurements were performed vdth both the A/8 and 3'A/8 standa: • .'cl susceptar.ces •

The measureda&ni ttonces were 00rrected ili accordance with equation (1) for displacement ·of the loop from the junction; both

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corrected and unoorrected values are plotted in Figs. 7 and 8. It will be seen that at. 500 Mo/sthe agr-eem.ent between admittanoe­meter and slotted-line measuren1ents was sometimes improved and . sometimes d.egraded by applying the oorreotion, so that on the average tr..e acouraoy was unaffected. At 900 Mo/s, however, where the oorrection is larger, it results in a useful improvement in. the aocuracy. .

5. Cone lus:i.ons

The absolute accuraoy of the admi ttanoe meter oannot be determ.l.r;\.;;d directly from the tests described in the previous section because the slotted li~e measurements are themselves subjeot to errors. However, it is unlikely that these en-ors will tend to .. reduoe the discrepanoy be~veen the line and meter measurements in the great majority of cases. It is therefore reasonable to assume

. that the error of the adni ttanoe meter oannot be greater than the largestdisorepanoy obsarved"

From measurement:! on nearly matohed impedances it may be deduced that the greatest error in measuring a perfectly matched load would be less than 4-% at frequencies up to 900 MC/s (i.e. the magnitude of the complex aClmi ttance error is less than 0.8 mmho. ) Moreover the error varies -but slowly with frequency (provided that a change from a 'A/8 to a 3'A/8 stub is not involved) and could be 0alibrated out on many applications.

The accuracy for pure susceptances 1S such that the error in measuring the lengGh of a 50 om transmission line will not exceed 1 cm. The error may be serious at 900 MC/s, where 1 cm is 0.2 radians. If, however, a simple correction is made for the displacement of the loop from the junction, in aocordance with equation (1), the error in length is reduced to 0.3 cm up to 500 11C/S, and 0.4- cm at 900 MC/s.

Measureme:nts were made, at 500 MC/s and 900 Mc/s, on a complete range of admittances giving a standing wave ratio of 0.3. The results are shovm in Figs. 7 and 8; it is impracticable to summarise them briefly.

The meter possesses the advantage of being more convenient to use than a slotted lill.eas measurements may be perfonned more rapid~, while less subsequent computation is required. It covers

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the range of frAqJ.encies which are 'b eyond the capabilities of a bridge, and for which slotted lines are ~conveniently long. The greatest objection to its use in this country is that its characte"::':i s+:ic impeclc'1.nce is 50 oms. This makes it inconvenient for measuring impedanoesseen through a length of 70 om cable. It would ?robably not be difficult to modify the me ter for use with 70 ohm cable "by reducing th6 diameter of the inner conductor of 1;00 unknovr.n arm only, and fitting a British. plug, '~'Uch as "Telconnectorll •

T.o obtain adequate sensitivity a . generator povrer ·of 100 roW is desirable & The. meter cannot therefore be used in the prescribed marmer to measure admi.ttances. such as rece:1.ver ~nputs for which a lower power leVel is required. There would, howeverpappea~to be no reasnn Vlhy this could not be accomplished by interchanging the . genera .... tor and detec tor ~

References

!lA direct reading ir;1pedance..ffieasU1"inginstrumen~ for the u.hof o' range'" ...

Type 874--1;,IR mixer rectifier"

3.. . tlVoHoF. and U.HIlF ... uIJi -!; oscillators"

General . Radio Experimenter, May, 1950 ..

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.APPENDIX I

The error due to the finite distance between the junction ana. the loops.

At high frequencies the distance between the junction and the loops becomes an appreoiable fraction of a wavelength and oannot therefore be disregarded. Although the line be~veen the loops and the j'L'11otion is non-uniforu, it may be regarded as equivalent to a uniform line of length CL (radians) with the same characteristio admittance (Yo ) as the rest of the system, and lli~ving the same total inductance as the existing arranGement. This is true because shunt capa~i ty at thej'1nction has no effect on the balance, since i tis in parallel with the generator. In the following argument powers of CL above the first \nll be neglected~

Suppose that- an unlmown admittance connected to the meter terminals presents an admittance Y = G+jB at the junction. Then if the voltage at the junction is V, the .current flowing into the unknown admittance and,measured by the loop is V(Y-jCLY

O)= V fG+j(B-CLYo)~.

Similarly the measured current in the standard conductance is VYO(l-jCL), and the standard susceptance is· adjusted in calibration so that its lli.aasured current has th,:;: same magnitude. 'rhus the current in the sta.'fJ.dard susceptance is f jVYo, the sign depending on· the nominal length (A/8 or 3A/8) of the line.

A null is obtained when

M:x!x + MGIG + MB IB = 0

where the 11: , MG and MB are the mutual inductancai betweenGhe loops and the innfu., conductors of the unknown, standard conductance and standard stlsceptence a:rmsrespectively. I, lG and lB are the corresponding measured currents. Substitu~ing the actual values of these currents we have.

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The apparent v~l~e of the a&~ittence, Y'=Gf+jB', which is given by the meter readinGs, l~ay be ob'tamed by neglecting a. :in the equation' (2 ).,

Thus

Substituting in equation (2) we have . . . . .' ' .

. JI~ . [G~j(B-ido).]~.MxGt(l-ja.) ~ jl,Y3' = 0

G G'

B = Br +a.(Y -G' ) o.

The .oorrectior:: to the susceptance is therefore It (Yo -G).

(3)

(1)

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APPENDIX 11

The effect of error in the s tanda£..d conductance

Let us suppose that the standard conductance presents an a&:1i ttance of Y +SG+,)cSB at the jtmction, where SG and ~B are small compared with Y~. If the standard susceptance is adjusted according to the procedure described in Section 2 its magnitude will be equal to the modulus of the admittance presented 1:y the standard conductance. Thus its value is +j(Y +SG), to the first order. Then with an unknovm admittance the gull condition will be

Now MG =: ~~G"/Yo and ";' ~,~ = ~'~"/Yo (see Appendix I) where G" + jB" is the apparent admittance measured.

Thus

G.- + jB - (G"/Yo)(Yo~G+jSB) - j(B"/Yo)(Yo-:,~G) = 0

. G =: G"(l+IG;Yo)

B = B"(l+SG/Yo) + G"SB/yo

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! "'5 drawmg! specification Is the property of the British Broadcaltlng Corporation and may not be reproduced or disclosed to a third party in any form wicflout the written per­mission of the Corporation.

GENERATOR

CONDUCTANCE STANDARD

REPORT No.G.OSI AP'D.

FIG. I

SUSCEPTANCE STANDARD

GENERAL ARRANGEMENT OF THE ADMITTANCE METER.

(REPRODUCED FROM THE MAKE.R'S INSTRUCTIONS)

UNKNOWN ADMITTANCE

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STANDARD CONDUCTANCE

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AXES OF LOOPS EDGES OF FARADAY SCREENS

SCALE: TWICE FULL SIZE

FIG.2 THE ADMITTANCE METER JUNCTION.

UNKNOWN ARM

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ISSUE I

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FIG.7

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COMPARISON OF MEASURED ADMITTANCES OF A MISMATCHED

TERMINATION AT 500 Mc/s

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ISSUE I

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FIG.S COMPARISON OF MEASURED ADMITTANCES OF A MISMATCHED

TERMINATION AT 900 Mc/s