CRMA Radiation Efficiency Based on Cavity Q-Factor

8/12/2019 CRMA Radiation Efficiency Based on Cavity Q-Factor

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Cyl i ndr i cal - Rectangul ar M crostr i p Ant enna - Radi at i onEf f i c i ency Based n Cavi t y Fact orC. M. Kr owneDept . of El ect r i cal Engi neer i ng, Nor t h Car ol i na St at e Uni v. , Ral ei gh,27650

I nt r oduc t i on: Radi at i on ef f i c i enc i es of a cyl i ndr i cal - r ectangul arm cr ost r i p ant enna depend n t he ohm c ( or di ssi pat i ve) l osses i n t hedi el ect r i cal subst r at e under l yi ng t he conduct i ng ant enna pat ch, and i nt he pat ch i t sel f and t he gr ound pl ane cyl i nder upon whi ch r est s t hedi el ectr i c subst r at e. Bel owwe wi l l onl y consi der conduct or ohm c l osses,as s m ng t he homogeneous di el ect r i c t o e per f ect l y l ossl ess. Theant enna i s anal yzed by f i r st t r eat i ng i t as a cavi t y wi t hwo el ect r i cwal l s ( at p=a and p=a+h; h=subst r at e t hi ckness) and f our magnet i c wal l sar e t hen combi ned wi t h a l umped- el ement equi val ent ci r cui t model( "open"; at z=O, - 2b and $=0, 29) . Cavi t y Q s der i ved f r om t hi s model( Fi gur e 1) of t he ant enna whi ch l eaks r adi at i on f r om t he f or mer l y per f ecmagnet i c wal l s. Fi gur e 2 shows t he ant enna cavi t y.Modal Cavi t yQ For an ant enna pat ch of l engt h 2b i n t he axi al-di r ect i on, ang%ir c i r cum er ent i al l engt h 8 i n t he $- di r ect i on, andr adi al wi dt h h i n t he p- di r ect i on, t he i deal l oss l ess cavi t y modal f i eare

cm = -J ' (koi ' a)/ J v' (km' a).w = wdi i s t he modal r esonant r adi an f r equency.

-V

CH1672-5/81/0000-00011 00.75 @ 1981 IEEE11


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e P I f i e l d solution i s

'p = - LFim E l(=)Rv(k8 m lp ) s i n ( $ + )s i n (% z ( 3d)H Q = - B m L i k n i R . ~ J ( k , i o ) c ~ s ( i ' ~9 . ; ) s in =b z ; H = i 3e)

Here kmi a r e t h e r o o t s of Rv(kmip) = 0 (p=a and a th ) , c i i of Eq. (2b)become cmi = -J-v(kmia)/Jv(kmia), Bmei is a co ns tan t fo r the mi i th mode,m=O,1,--- and k = 1 , 2 , - - - .

Define the mlli t h mode as g iven by the per tu rba t iona l expre ss iondi d / P d 4 )

where [rl is t he to t a l s to r ed cav i ty energyand 7, he time-average di ss ip at edDowery theconductors (Eq. 4) s eva lua t edu smg h eunper tu rbed i e ldsof Eqs. (1) - (3) ) . For TEz modes,

a+h 23= E I 1 d $ I dz(lEG12 lE+I2) J d0 -2b

Here R is t heconducto rsu rfa ce es ist an ce . Combining Eqs. (l), 2) , 4 ) ,and 5 ) , and using Bess el funct ion propert ies ' al lows i t o b e w r i t t e n as

M modal Q caneound by addin g IE t o h e Eq. (5a) i n t eg rand ,coun t ingon ly hp&angen t i a l H co ntr ibu t io ns Za t p=a and a+h i n h e Eq. (5b)integrand, and using Eqs. 2 ) - t 4 ) .

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Note t hat Eq. ( 7a) shoul d be eval uated by repl aci ng- by the Besself unct i on N of t he second ki nd t o mai nt ai n l i near i nde; endencen Eqs. (2).Modal Radi at i on Ef f i ci ency: Fi gur e model s t he ant enna as a 2- por t net -work by usi ng a par al l el l umped- el ement ci r cui t equi val ent . The r adi at i onadm t t ance Y = Gr + j Br account s f or t he t i me- aver age r adi at i on powerosst hr ough G akd B cont ai ns bot h t he i deal cavi t y suscept ance and t her adi at i onr suscep%ance cont r i but i on dueo t he l eaky cavi t y3. R account sf or ohm c l o s s e s i n t he conduct i ng cavi t y wal l s. t is possi bl g t hat Gnay al so haveo account f or waves l aunched as di el ect r i c sur f ace- gui de2waves.t i me- average t ot al di ssi pated power by t he net wor k gi vesDef i ni ng as t he r at i o of t he t i me- aver age r adi at ed powerto the

= Pr / P = (P-P )/P = 1 - P / P (8)wher e P i s t he t i me- ver age power di ssi pat edy t he r esi st ance R. Si ncePC =( l / hRe[vI c*l = Vl 1 2Rw andP=(l/2)Re[VI*]=IVI2(Rw-'+cr)/2, w

as t he r at i o of t he t i mg- aver age r eact i ve powero t he ti me- aver age di ssi -A qual i t y f actor Q can be def i ned f or t he ant enna equi val ent net wor kpat ed power :(10)c = I mVI *] / Re[VI *]=R Bw r

Combi ni ng Eqs. 9 ) and 10) yi el ds f or t he r adi at i on ef f i c i ency of t hem th mode

spacecraf t , and ai r cr af t conf or mal cr os t r i p ant enna pat ches ar e used.Concl usi on: I n many appl i cat i onsper t ai ni ng t o sat el l i t es, m ss i l es ,Knowl edge of t he r adi at i on behavi or of cyl i ndr i cal - r ect angul ar m cr ost r iant ennas cont r i but es t on under st andi ng of r adi at i on f r om cur ved pat chant ennas, and i n par t i cul ar , t o an under st andi ng of r adi at i on f r om apat ch on a cyl i ndr i cal sur f ace whi ch has a ci r cul ar cr oss- sect i on nor malef f i c i ency f or r adi at i on f t he ml i t h cavi t ymode. Thi s anal ysi s hast o t he cyl i ndr i cal axi ali r ect i on. Her e we have det er m ned t he modalassumed t hat t he l eakagef ener gy f r om t he cavi t y i s smal l enoughot hat t he use of cavi t y modes t o char act er i ze t he r adi at i onm i as wel las t he useof t hese modes i n f i ndi ng i s a good appr oxi mat r on. Oneexpect s t he appr oxi mat i ono be excel dnt when h


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References1 D. L . Kreider, R. G. K u l l e r , D. R . Ostberg and P W Perkins,

1966), pp. 773.Introductionto Linear Analysis Addison-Wesley,Reading, Ha2. C H Krone, E-Plane Coupling Between Two Rectangular Micros

Antennas , Electron.Lett., 1980,Vol.16, pp. 635-636.

I+O ___

Y v yr.-Figure 1 Equivalent circuit model of antenna.

Figure 2 . Cylindrical-rectangularantenna avity.

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CRMA Radiation Efficiency Based on Cavity Q-Factor