THE ANL=YSIS OF CIRCULATOR FmREQUNCY SHIFT WITH THE

TEEPERATURE VARIATION.

SAJIN GEORGE

ABSTRAT.- Starting from the fundamental relationships thatgovern the microwave circulator design one oan derive theformula of the working frequency. An analztioal expregsionfor the relative frequeney shift vs.temperature variationsis inferred, The variation of effective permeability of fer-rites and that of the working frequency of the circulator inthe -2O0C.. .+600C temperature range is plotted. The experi-ments demonstrate a good concordanoe with the theory.

I INFLUENCE OP THE TWPERURE VARIATIONS ON THE WORKINGPR OQUFICYOF CIRLATORS.

According to the data from the xpecialised literature, I ,for the fundamental mode of resonance of the circulator fer-rite disc,the following relationships are established:

klR a 1*84 (1)2Wf!k /Uff f (2)

2 -K2/Ueff /- (3

where the notations are those established in the specialisedliterature:

R : ferrite disc radius,fc: working frequency at 2000,:fs relative peittivity of ferrite,a a speed of light in free space,

u nd K : elements of Polder tenser,written a:

Hi*4zX (2 _}2 a2/4-i+ Hi.to4WX53(Hi -aH * AH2I4) 4

(Hi - H2 _ AH2/4)2 + i4 ARE2

Research Institute for Electronic Components (ICCE)Str.Erou Ianou Nicolse 32B,s*ector 2,Buoharest,Romania.

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-H0.4tX1 - RH2 _E2 /4)(H2 _ 2 _ AH2/4)2 +2HLH2

± 0 i4R a

In (4) ed (5) the following notations are used:Hi : internel magnetic field in ferrite,

4 ThE : ferrite saturtion magnetisation,AH : ferrit inewidth,

He : gmagetli resonane field.

The working frequency of the circulator results explioitlyfrom relations (1) and (2):

f Sl8o(6)C 21ZR /Ueff 6f

An analysis of the relation (6) shown that the *elemnts sgms-ceptible of being affected by the temperature are the ferri-te radius,Rthe ferrite pemttivity, d1, and the effectivepermeability /Uff*

The bibliographioal data about the dependenoe f vs. tempe-rature are not known and therefore one can consider that therelative permittivity of ferrit* is temperature independent.The dimensional variations of ferrite radius due to the di-latations and contraotions induoe a negligible effect on theciroulator workig frequency.

The effective permeability variations with the temperaturechanges are induced through the Pelder tensor elementsand K, by the variation of the ferrite magnetisation. In atemperature range t1...t2 (t1 < t2), ,uff will vary be-values,2 an eff

oftween two falues%fUf(tl) an /eff (t2). Adequately,thecirculator frequency will be:

(7)l.8&o I~~~~.84oaC I 2itR Cf/eft) f0(t2) 22WR c.uf(2

Relative frequency shift in the tomperature range tl...t2 is:

Af |jaf(t1) -jy(t2)1 (8)

f ffc

404

whioh,after some maipulations,yieldus

/Uerr,(20 I'u ,u '"

2 * GOEPTA NS.ll K RIMINAL RFSUL

Relations (3),(4),(6) and (9) may be used,by their introduc-tion into a computer progrp to plot the Workin frequencyvs. temperature. It is ncessar to know the saturation sag-

netisation variati-on with temperature.

1100

1000 B

900 _----Ah - --

800

700

600- -- , *- -- i

leff Fig.I V.ariationsof aagnetisation,

I|effectiv permeabi-2 _ -__1 _ ____ lity and frequency

vs. temperature fora substituted gar-

1,5 ____________________________

net (A) and a spi-nel (B).

1300f 1MHz]

405

I p , A a a a I A

-20 -10 0 10 20 30 40 50 60 TOC

T!he variations of effective permeability and of frequencyvs. temperature were plotted for two ferrite sampless a sub-stituted garet (A) and a spinel (B),whose saturation magne-tisation cages with temperature are presented in fig.l.The computations of frequency shift were effeoted for an abo-ve resonance circulator structure at frequency f0 = 1200 MHs.Data on ferrites used in computation -are presented in tab.I.

Table I. Ferrite material data.

Mlaterial 4ftiLN (Go) aH (°) sr I

A 900 180 15B ~~~900 120 12

The study of curve of fig.l shows that the material (A) preseats a reduced magnetisation ohanges in the temperaturerange -200C0..+4000. Over that range the effective permeabi-lity vary between 1.96 at -200O and approx. 2 at +6000,im-plying a frequency shift between 1215 MHznsd 1198 VHs.The relative frequency shift in this temperature range is:

a f ) 1215-1198

One can notice that in the +200C.*.+6000 temperature domainthe frequency remains almost constant,this pemitting thework at high power levels,where the insertion losses.eventhey are small.,may produoe a ferrite warming.

The material (B) - a tUg spinel - presents a pronounced sa-turation magnetisation variation,between 1180 Gs at -200Cand 640 Gs at +6000 (xee fig.l). This leads to an *ffeotivepermeability change between 2.3 and 1*78,that implies a fre-quenoy shift between 1120 MHz and 1293 MHs. The relativefrequency shift in this temperature range is:

A f =1293-12Tf (%) 12ft U0x 1l00 14.43 %

This frequency shift is large enough to deteriorate the mainfunctional parameters of ciroulator (isolation and insertionloas) at the eadge of temperature range.

In fig.2 an experiment effected with a type (B) ferrite with

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which a oiroulator on 1190 IMs was made,is shown. Threeplots of isolation and insertion loss at s200C,+2000 and+6000 were *ffected. One can notice a frequency shift be-tween 1120 INs and 1300 s in this temperature range andsiml3taneously a deterioration of funotional parameters,especially of isolation,whioh deoreases below 20 dB at +600a.

-200C[dB]| l + 200C40 +/60%C

-4

1100 1120 1190 1300 fftvMHz]

Fig.2. Isolation and insertion losses for a circulatoron 1190 Is,at temperature of -20OC, +2000 and +6000.By computing the relative frequency shift one finds:

-y--(%) ,= -322lrjo1120zl0Qn 15.l %

A good agreement is noticed between this experimentallyfound value and the relative frequency shift computed forthis material with the aid of (9).

1. BOSIA HK On Stripline 7 Circulation at UN?.IEEE Trans.on ITT, Vol*JT-12,p.61lJan*1964.

2. GARDIOL MRED : Lea ferrites en hyperfrequencesRevue "RF",Vol.II,nr.3,p.1

3. LAX B. BUTTON KR.: Microwavw Ferrites and FerrimagneticsNewYork,MoGraw Hill Book Comp.1962.

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