Definition1: The ratio of the radiation intensity in a given direction from the antenna to the radiation intensity averaged over all directions.

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Tobias Watts
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1 Dirctivity or Dirctiv Gain. 1

2 Dfinition1: Dirctivity Th ratio of th radiation intnsity in a givn dirction from th antnna to th radiation intnsity avragd ovr all dirctions. Dfinition2: Th avg U is obtaind by powr radiatd by 4π,(rad int of isotropic antnna) Th ratio of its radiation intnsity (U) in a givn dirction ovr that of an isotropic sourc. D = U/U 0

3 Antnna Dirctivity Total powr radiatd P rad Avrag radiation intnsity U 2 0 avg 0 U(, )sindd Prad 4 D U U U avg P rad 4 NOTE: D Has no units

4 Antnna Dirctivity Dfinition3: If th dirction is not spcifid thn w calculat dirctivity in th dirction of maxima Th ratio of radiation intnsity in max. dirction to th radiation intnsity of isotropic sourc. (D 0 ) Dmax= D 0 = D=dirctivity Do= U=radiation intnsity Umax= Uo= Prad= Umax/U 0 = 4π Umax/ P rad P

5 Proprtis of D D=1 for isotropic sourc D>1 for non isotropic (max. dirctivity is gratr than 1, Umax>Uo) D= 4π / Ω A smallr th bam ara..

6 Antnna Radiation Efficincy Conduction and dilctric losss of an antnna ( I 2 R losss) = cd fficincy. Lt R cd rprsnt th actual losss du to conduction and dilctric hating. Thn th fficincy is givn as K / cd P P rad in R cd R rad R rad Practically losss ar thr, so R cd R rad R cd Practical antnna: K<1 Idal antnna: K=1

7 Ovrall Antnna Efficincy Th ovrall antnna fficincy is a cofficint that accounts for all th diffrnt losss prsnt in an antnna systm. p r c d cd p t r c d polarization rflction conduction dilctric losss losss mismatchs conductor& dilctric If antnna is prfctly matchd, r=0 t = cd. p r cd fficincy ( impdanc mismatch) losss

8 Rflction Efficincy Th rflction fficincy through a rflction cofficint (G) at th input (or fd) to th antnna. r R R 1 input R R output input input 2 R R gnrator gnrator antnna input impdanc( ) gnrator output impdanc( )

9 Dirctivity= Gain= D Antnna Gain D P in 4U P rad 4U W know K=Prad/Pin G= K 4U P rad So

10 Gain It can b masurd by comparing radiation intnsity of th antnna undr tst (AUT) with a rfrnc antnna. Rf antnna =dipol, horn (whos gain can b calculatd) G= U(AUT)/U(rf) If rf antnna is isotropic G=U(AUT)/Pin/4π G= 4π U (AUT)/Pin

11 Antnna Gain Th dirctivity and gain ar masurs of th ability of an antnna to concntrat powr in a particular dirction. Dirctivity powr radiatd by antnna (P 0 ) Gain powr dlivrd to antnna (P T ) G K KD P P rad K: radiation fficincy (50% - 75%) G has no units Usually rlats to th pak dirctivity of th main radiation lob Oftn xprssd in db Known as Absolut Gain or Isotropic Gain in 11

12 Gain Antnnas Gain Th powr gain, G, of an antnna is vry much lik its dirctiv gain, but also taks into account fficincy G, D, Th maximum powr gain G max D max Th maximum powr gain is oftn xprssd in db. G max db 10log G 10 max

13 Exampl D8.3: Suppos an antnna has D = 4, R rad = 40 and R diss = 10. Find antnna fficincy and maximum powr gain. (Ans: = 0.80, G max = 3.2). Antnna fficincy R rad R rad R diss (or) 80% Maximum powr gain Gmax Dmax Maximum powr gain in db G max G db 10 log 10 log max 10

14 14 PFD vs. Antnna Gain S 0 = PFD producd by a loss-lss isotropic radiator ), ( 4 ), ( ), ( ) )( ( ), ( ), ( S G r P G r r r S

15 Othr Dfinitions of Gain For practical purposs, th antnna gain is dfind as th ratio (usually in db), of th powr rquird at th input of a lossfr rfrnc antnna to th powr supplid to th input of th givn antnna to produc, in a givn dirction, th sam fild strngth or th sam powr flux-dnsity at th sam distanc. Whn not spcifid othrwis, th gain rfrs to th dirction of maximum radiation. Th gain may b considrd for a spcifid polarization. [RR 154] 15

16 Antnna Gain Actual antnna Masuring quipmnt Rfrnc antnna Masuring quipmnt P = Powr Dlivrd to th antnna S = Powr rcivd at a grat distanc P o = Powr Dlivrd to th antnna S = Powr rcivd at a grat distanc Antnna Gain (in th spcific dirction) = P / P o 16

17 Rfrnc Antnnas Isotropic radiator isolatd in spac (G i, absolut gain, or isotropic gain) Half-wav dipol isolatd in spac, whos quatorial plan of symmtry contains th givn dirction (G d ) Short vrtical antnna (much shortr than /4), clos to, and normal to a prfctly conducting plan which contains th givn dirction (G v ) 17

18 Rfrnc Antnnas (1) Isotropic antnna Snds (rcivs) nrgy qually in (from) all dirctions Gain = 1 (= 0 db) Whn supplid by P, producs at distanc r powr flux dnsity = P /(4r 2 ) Thortical concpt, cannot b physically ralizd Radiation pattrn in vrtical plan Radiation pattrn In horizontal plan 18

19 Rfrnc Antnnas (2) Half-Wav Dipol Linar antnna, ralizabl Gain = 1.64 (= 2,15 db) in th dirction of maximum radiation Figur-ight-shapd radiation pattrn in th dipol plan, omnidirctional (circular) in th orthogonal plan Radiation pattrn in vrtical plan Radiation pattrn In horizontal plan 19

20 Effctiv aprtur and aprtur fficincy Rciving antnna xtracts powr from incidnt wav P rc S in A Aprtur and bam ara ar linkd: A 2 A For som antnnas, thr is a clar physical aprtur and an aprtur fficincy can b dfind ap A A p

21 Rciprocity Transmission and rcption antnnas can b usd intrchangably Mdium must b linar, passiv and isotropic Cavat: Antnnas ar usually optimisd for rcption or transmission not both!

22 Rciving Antnnas and Rciprocity r For a linar two-port V 1 =Z 11 I 1 + Z 12 I 2 V 2 =Z 21 I 1 + Z 22 I 2 If I 2 = 0, V 2 = Z 12 I 1 ~ 1/r For r larg, Z 12 << Z 11, Z 22 + V 1 - Rciprocity Z 12 = Z 21 Equivalnt Circuit I 1 I 2 + Z 11 -Z 12 Z 22 -Z 12 Z 12 V 2 -

23 Circuit Rlation for Radiation into Fr Spac Z 11 -Z 12 Z 22 -Z I 1 V 1 Z 12 V 2 (opn circuit) - - V 1 = V Z 11 I 2 = V OC = Z 12 I 1 1 Transmittd powr * 2 P T 1/2 RV 1 I 1 1/2 R Z 11 I 1 (1/2)R r1 I 1 whr R r1 radiation rsistanc of antnna 1 2 Thrfor : Z 11 R r1 jx 1 Similarily : Z 22 R r2 jx 2 whr R r2 radiation rsistanc of antnna 2

24 Rcivd Powr and Path Loss Ratio Z 11 -Z 12 + Z 22 -Z I 1 V 1 Z 12 V I 2 V 2 Z 22 * Matchd Load R r2 - jx 2 Z 12 Currnt I 1 divids btwn branchs: I 2 = -I 1 Z 12 Z 22 Z 12 Z 22 Rcivd Powr for Matchd Load P R 1 2 I 2 2 Rr I 1 I 1 Z 12 2R r 2 2 Z 12 2R r 2 I 1 2 Z R r 2 Path Gain PG P R P T I 1 2 Z12 2 8Rr 2 I 1 2 Rr1 2 Z R r1 R r 2 Final xprssion for PG is th sam if antnna 2 radiats and antnna 1 rcivs.

25 Effctiv Ara of Rciving Antnna Effctiv Ara = A g, P R P a r A P T 4 r 2 A A 1 P T Z * 22 Z * 11 P T A 2 PG P R P T g A r and by rciprocity PG P R g A P T 4r 2 Thrfor g 2 A 1 g 1 A 2 or A 1 g 1 A 2 g 2 sam for all antnnas

Impedance Transformation and Parameter Relations

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