Antennas produce fields which add in phase at certain points of space. Consider a loop of wire that carries a current. R 1 R 2. R 2 -R 1 0.1λ. D 0.

Transcription

1 Module 6: Antennas

2 6. ntoduction n chapte, the fundamental concepts associated with electomagnetic adiation wee examined. n this chapte, basic antenna concepts will be eviewed, and seveal types of antennas will be examined. n paticula, the antennas commonly used in making EMC-elated measuements will be emphasized. 6. The Radiation Mechanism Antennas poduce fields which add in phase at cetain points of space. Conside a loop of wie that caies a cuent. d R D R d Hee two elements of cuent d and d ae sepaated by a distance D. The cuent elements ae located at distances R and R, espectively fom a distant obsevation point. f R -R.λ D.λ Then the fields poduced by the cuent elements add out of phase, and the amount of adiation is small. Howeve, if R -R.λ D.λ Then the fields poduced by the cuent elements add in phase, and the amount of adiation is lage. -Reception Mechanism Electomagnetic fields which ae incident upon an antenna induce cuents on the suface of the antenna which delive powe to the antenna load. 6-

3 induced cuent incident field tansmission line L load impedance antenna 6. Radiated Powe The powe adiated by a distibution of souces is that powe which passes though a sphee of infinite adius. This, theefoe, is the powe which leaves the vicinity of the souce system, and neve etuns. n chapte the time-aveage Poynting vecto was pesented P E H R e At points fa fom the antenna (the adiation zone) { } jk e ( ) jω [ N + φ N φ ] E µ whee H ( ) E ( ) η jk ( ) (, φ) ( ) S N J e d v v is known as the adiation vecto. The adiation vecto is elated to the vecto potential by with (,, φ) N (, φ) A µ e jk 6-

4 Now in the adiation zone jk µ e jk ( ) A( ) J ( ) S e d v P E R e v E η Using the vecto identity A ( B C ) B ( A C ) C ( A B ) {( ) ( ) } P E E E E η R e Finally E E η...because E [ N N N φ N φ ] ωµ + η...because [ N + φ N φ ] [ N + φ N φ ] [ N N + N φ N φ ] η P N + N 8λ φ This epesents the aveage powe flow density and lies in the diection of wave popagation. The powe adiated though a sphee of infinite adius is given by lim n P ds s Applying the expession fo the time aveage Poynting vecto leads to π π η N + N lim d d φ sin φ 8λ 6-3

5 π π η + N N φ λ sin d d φ 8 Let K d η N + d Ω λ 8 N φ... adiation intensity powe adiated pe unit solid angle....whee dω sin ddφ. The total adiated powe is then π π ( φ ) K, d Ω. 6.3 Antenna Teminology Antenna Pattens Radiation patten - A plot of the adiation chaacteistics of an antenna. Thee ae two types of adiation pattens:. Powe patten - A plot of the adiated powe at a constant adius.. Field patten - A plot of the electic o magnetic field magnitude at a constant adius. An antenna patten consists of a numbe of lobes. The lagest lobe is usually called the main lobe, while the othe smalle lobes ae called side lobes. The minima between lobes ae called nulls. main lobe side lobe null Radiation pattens ae thee-dimensional, but ae usually measued and displayed as two- 6-4

6 dimensional pattens, which ae sometimes called cuts. Fo most antennas, two cuts give a good epesentation of the thee-dimensional patten. The adiation pattens of linealy polaized antennas ae often specified in tems of E- plane and H-plane pattens. The E-plane contains the diection of maximum adiation and the electic field vecto. The H-plane contains the diection of maximum adiation and the magnetic field vecto. E-plane E H H-plane No antenna has a tuly isotopic patten (one which is the same in all diections). Rathe antennas (eal ones anyway) tend to adiate moe effectively in some diections athe than othes. Diective gain - The atio of the adiation intensity K(,φ) to the unifom adiation intensity fo an isotopic adiato with the same total adiation powe....whee g d (, φ ) (, φ ) K K (, φ ) is the total powe adiated by an isotopic adiato pe unit solid angle. Diectivity - The maximum value of diective gain. Gain - Diectivity expessed in db. G log (diectivity) gain in db Beamwidth - The beamwidth of a adiation patten is the angle between the half-powe points of the patten. 6-5

7 3 db (half powe) points φ side lobe Radiation efficiency - The adiation efficiency of an antenna is the atio of the powe adiated by the antenna to the total powe supplied to the antenna. The total powe supplied to the antenna consists of the powe adiated and the powe given up to esistive losses. E + L...whee E adiation efficiency powe adiated L powe lost Radiation esistance - The adiation esistance of an antenna is the equivalent esistance though which its input cuent must flow in ode that the powe dissipated in the esistance is equal to the total adiated powe. R o R...adiation esistance...whee is the input cuent to the antenna. Fom the stand point of the souce that dives an antenna, adiation esistance is indistinguishable fom Ohmic esistance. n both cases, the souce must continuously supply enegy to the antenna in ode to keep the cuent amplitude constant with time. n the case of Ohmic esistance, this esistance convets enegy into popagating electomagnetic waves. nput impedance - An abitay antenna with a pai of input teminals a and b is shown below. 6-6

8 in a b V in Antenna hen the antenna is not eceiving powe fom waves geneated by othe souces the Thevenin equivalent cicuit looking into the teminals of the antenna consists only of an impedance in V R in + jx in whee R in is the input esistance and X in is the input eactance. The input esistance is the sum of two components Rin R i + R L whee R i is the input adiation esistance and R L is the input loss esistance. R L accounts fo that potion of the input powe that is dissipated as heat, while the input adiation esistance R i accounts fo powe that is adiated by the antenna. R i is elated to R by in Radiation efficiency can be expessed 6.4 Hetzian Dipole η R i m ax P P a d in R i R. R i + R L. The simplest adiation souce consists of a shot segment of cuent 6-7

9 z d z A, B, E d z y d z x A Hetzian dipole consists of a unifom cuent flowing in a shot wie dz teminated by point chages. Hee t is seen that d z d z z x y J ( ) fo z δ δ e lse w h ee ( ) ( ) ( ) δ( ) J d s δ x y d xd y x y The chage associated with the cuent is found using the continuity equation The cuent density may be expessed J jωρ ρ jω d J z d z J zδ ( x ) δ( y) u z + d z d z u z whee u(t) epesents the unit step function. 6-8

10 J d z d z z ρ ( ) ( ) ω δ δ d x y u z j d y + d z d z u z d z ( ) ( ) + + d z x y z z jω δ δ δ δ...because du( t) dt δ( t) z d z z (+) point chage at, (-) point chage at d z Vecto potential whee so, o jkr µ e A( ) J ( ) R dv R v fo >> d z jk µ e A( ) J ( ) d v jk µ e δ ( x ) δ ( y ) d x d y z d z x y µ A( ) z dz e v jk dz dz z 6-9

11 ! # #!!! now use z cos sin to get ( ) ( c os sin ) jk A µ d z e E-M fields B φ A A ( A ) µ φ jk dz ( sin e ) µ φ d z + π jk sin 4 e co s sin e jk jk so B φ µ d z jk + jk sin e E j ωµ ε B at all points whee J ( Bφ sin ) ( B φ) j ωµ ε sin j d z ωε sin + jk jk + jk sin e sin e jk " E j dz + jk e sin cos ωε sin jk j k jk sin [ + jk ] + jk e jk 6-

12 $! % '!! (!! ( & ( j ωε d z + jk 3 + jk k co s + sin 3 e jk now use Then ωε ω µ ε...whee η k E d z e jk η + jωε µ ε η µ ε jk d z e η co s + jωµ + + jωε sin. Thus the fields may be expessed: $ B d z jk φ µ sin + e jk E dz η co s j k e jk 3 E d z jk π η + sin 4 j k e jk 3 t is seen that these expessions contain tems having thee diffeent ates of decay: /, /, and / 3. Nea-zone fields (induction zone) << λ π The nea zone fields ae those which ae stongest nea, o when. Thus these ae the tems of B which vay as / and the tems of E which vay as / 3 : [ co s sin ] E j d z e jk η 3 + k ' B e φ µ d z sin jk 6-

13 & ) ( +, & The nea zone E -field looks like the field of an electostatic dipole. The nea zone fields do not contibute to adiated powe. nstead they esult in eactive powe (time changing enegy stoed in the fields nea the antenna). Only the / tems contibute to adiated powe. Fa-zone fields (adiation zone fields) The fa-zone fields ae those which ae stongest as of E and B which vay as /: ' jk d z e B φ µ jk sin. Thus, these ae the tems * E jk dz e sin η jk The adiation zone fields ae those that contibute to adiated powe. Note that fields fom a tansvese wave. Radiated Powe / B lim n, P - ds s - P { E - H - } R e.. whee n and d s dω has tems that go as / and / and E has tems that go as /, / and / 3. Since d s as only the / tems contibute to. - - lim Re{ E H } d Ω whee E and H ae the / tems fom E and H called the adiation zone fields. π π E H d φ Ω 6-

14 6 d z π π ωµ k sin sin sin d d φ dz 8 k 6π ωµ π 3 π π 3 k d sin d d z 4 ωµ π φ use: π µ ωµ ω µ ε kη ε dz π k η use: k π λ η π 3 d z λ atts Radiation esistance d z λ R η π 3 d z λ o R η π d z 8π 3 λ d z λ Example: Calculate the adiation esistance of a cm length of unifom cuent if the fequency is 9 MHz and the host medium is ai: 8 c 3 m λ s cm f 9 H z R 8π m m Ω t is seen that the adiation esistance of a shot cuent segment is only on the ode of a faction 6-3

15 of an Ohm, making it a elatively inefficient adiato. Diective gain g d ( ) K ( ) / π π K ( ) d Ω g d ( ) dz [ ωµ ][ k ] π sin sin 4 dz 4 4 ωµ k ( π ) ( π ) π π g d ( ) 3 sin sin Diectivity π D m ax [ g ( ) d ] g d Radiation fom a cylindical dipole G gain log ( 5. ) 76. db The cylindical dipole antenna is one of the most commonly used antenna in the VHF/UHF fequency ange. The cylindical dipole may be viewed as an open-ended tansmission line which has been flaed out. (z) + V g - R g l z Open cicuited tansmission line 6-4

16 9 zl (z) + V g - R g + V - z Dipole antenna z-l Fa zone fields 8 z zl ( z ) 8 R B ( ), E ( ) + 9 V _ y x ( ) z-l t is noted that z ± l (cuent at the tips of the antenna is zeo). 6-5

17 < A : C < < < < D < < > ; E > < H The cuent density pesent on the dipole is given by The adiation vecto is whee? ( ) ( ) ( ) : : z z x y ; fo z l J ( ) δ δ elsew h ee...whee ( z ) ( z ) sin k l sin kl : : : jk ( ) (, φ) ( ) N J e d v ABA z z ( z ) z co s : N Using the elationship gives Let then (, φ) δ ( ) δ( ) sin ( ) v z jkz co s x y dx d y k l z e d z sin kl l x y l l z l z jkz co s sin k ( l z ) e d z sin kl z l z jkz co s z jkz co s sin k ( l z ) e dz + sin k ( l + z ) e d z sin kl sin kl ax ax e e sin( b x + c) d x a ( b x c) b ( b x c) sin + co s + a + b F : N (, kl) N (, φ) z z k sin kl co s( kl co s ) co s kl sin (, φ ) l [ ] co s( kl co s ) co s kl sin adiation function (, kl) ( co s sin ) F k sin kl sin FGF z FF 6-6

18 < < < < jk e < < ( ) j [ N + φ N φ] : : E jωµ πk e jk ω µ F whee F (, kl) (, kl) < J...fa zone E -field co s( kl co s ) co s( kl) sin( kl) sin Use ωµ kη then : : : : H ( ) : : E ( ) jωµ η πkη ( ) F (, kl) E : : jη π jk e jk j e φ π F ( ) (, kl) H e jk F (, k l) φ Radiation zone fields poduced by a dipole Radiation patten so K η K (, φ ) N + N 8 λ η η 8 λ 8 λ ( ) N F (, kl) 4 k φ η π F 8 (, kl) (, ) K ( φ ) K φ Often times is plotted as opposed to, since K descibes the patten of the fa-zone field: co s( kl co s ) co s kl K ( ) F (, kl) sin 4 x x co s x + + K! 4! 6-7

19 Special case: kl << l << λ F ( kl co s ) + ( kl) << sin ( kl) [ co s ] (, kl ) ( kl) sin sin Same patten as Hetzian dipole. z.77 powe point 9 L 9L boadside diection b eamwidth 9L Othe cases: 6-8

20 l lam bda/ l lam bda l (3/)lam bda 4 7 llam bda Most often the length lλ/4 (half-wave dipole) is used, since if it is a nealy esonant stuctue with its cuent maximum at the diving point (z). Fo a dipole with a non-zeo wie adius, the length must be slightly shote than λ/4 to poduce esonance. 3 Note if we define the input impedance in as V in input voltage input cuent then esonance occus when is puely eal (just as in cicuit theoy). Radiated powe π π π π K ( φ ) d η d φ, Ω F (, kl) sin d π 8 φ π η F (, kl) sin d This expession must be integated numeically. Special case #: kl<< (Shot dipole) F (, kl) ( kl) sin 6-9

21 P M Q N Q η 4 ( kl) π 3 sin MON P d η πω 4 3 ( π) 4 π 4 l λ lπ 4 λ 3 atts Special case #: thus kl π F, π (Half-wave dipole) π π co s co s co s π sin sin η π co s PPRP π co s d sin PPSP. by numeical integation π co s co s sin Diectivity D { K ( )} m ax Special case #: kl<< (Shot dipole) η η π, π 8 8 sin K ( ) F ( kl) ( kl) 6-

22 so π K ( ) K η ( kl) m ax 8 π 4 D η ( kl) π 8 4 ( kl) π η ( ) ( ) G log D log 3. 76dB 3 Special case #: kl π (half-wave dipole) D K ( ) m ax η 8 π π η 4 π K η 8 π (. ) η 8 π. 64. π π co s co s π sin moe diective than shot dipole G log (. 64). 5dB Radiation esistance R 6-

23 Special case #: kl<< (shot dipole) π ( ) 6 F, kl sind π R ( kl) 6 d sin sin l 8π λ Ω Special case #: kl π (half-wave dipole) (. ) 36 6 R 73. Ω Note that a esonant half-wave dipole ( in R in + jx in j) is matched quite well by a 75Ω coaxial cable tansmission line. Example l hat input cuents ae needed to a shot dipole of length and to a half-wave λ dipole to adiate a powe of k? R shot dipole: R 8π 7. 9Ω 5. 9 A half-wave dipole: R 73. Ω 5. 3A 6.6 Radiation fom a small loop antenna 6-

24 X T X X z U U U U E ( ), B( ) V T U R a y x The fields associated with a small loop antenna can be shown to be ( k a ) E ( ) φ η 4 e jk sin H ( ) E ( ) ( k a ) e η 4 jk sin Radiated Powe η η K (, φ ) K ( ) N + N N λ 8 8 λ φ φ η 8 λ ( π ) k a sin π using η π λ k π K (, φ ) 5 ( ka ) sin

25 Y [ Note that the adiation patten of the small loop is identical to the adiation patten of the Hetzian dipole. The small loop is the magnetic dipole analog of the electic (Hetzian) dipole π 5π 4 3 K ( ) dω d φ ( ka ) sin d 4 φ π 5π π 4 3 ( ka) sin d [ \ π ( ka) atts Radiation esistance R π ( ka ) Ω 4 [ ] example: a 4 λ. 5 R π π (. 5) 9. Ω Diectivity Since the adiation patten of the small loop is the same as that of the Hetzian dipole, the diective gain, the diectivity, and the gain ae the same: D 3/ G.76dB 6.7 Cuents above a pefectly conducting gound Antennas ae often placed above conducting sufaces, fo puposes of measuements in the lab, o in pactical situations as when an antenna is placed on a ca oof. Often the eath itself is modeled as a pefect conducto (although this not always a good appoximation because the conductivity of the eath is faily low). Fields poduced by cuents by antennas above a gound plane can be calculated using the method of images. Method of images Conside a cuent caying element above a pefectly conducting plane: 6-4

26 V V z E, B? ] ] p efect conducto, E B x ^ E The cuent element will poduce an -field which will induce cuents to flow on the suface of the conducto. These cuents will poduce an additional scatteed field. The total field must obey the bounday condition E tang ential on the conducto suface at z. e may eplace the poblem by an equivalent poblem. The gound plane is emoved and eplaced by an image cuent. z Fee space x Fee space "image" cuent Hee the fields poduced by both the cuent and its image will be identical to the fields poduced by the cuent above the gound plane as long as the bounday condition on the total field E tan at z is obeyed. Question: hat image cuent will esult in the bounday condition being satisfied? Since any cuent distibution can be viewed as a supeposition of Hetzian dipoles, we only need to identify the image of a Hetzian dipole. The field due to a Hetzian dipole on the z-axis is given by 6-5

27 X a a ` X ` E d z e jk η + jωε Case : Hoizontal dipole jk d z e η co s + jωµ + + jωε sin d E, E i E, E i d i i E i E i E E i i i i i choose: d i d,, i i thus:, i i ( ) ( ) ( E ) ( E ) and: E E, i tan ( ) tan So, E + then bounday condition is satisfied. E i tan i tan tan 6-6

28 d d b b c c b b Case : Vetical dipole d E, E i E, E i E d i i i E i i i E E i i i choose: d i d,, i i thus: i, π i cos i cos ( ) ( ) ( E ) ( E ) and: E E, i tan ( ) tan So, E + then bounday condition is satisfied. E i tan i tan tan Summay:. Hoizontal cuents image in opposite diections.. Vetical cuents image in the same diection. 6-7

29 e e 6.8 Monopole above a gound plane fee space l E, B? coaxial cable The equivalent poblem is a dipole. l l i Thus the fields adiated by a monopole above a gound plane ae identical to those of a dipole in fee space. Howeve, the adiated powe, and thus the adiation esistance ae half that of the dipole, since the monopole only adiates into half the space that the dipole does. m o nopole dipole η F (, kl) sin d π R R 6 F ( kl) d m on op loe dip ole, sin π 6.9 Boadband antennas Although dipole antennas possess many attactive chaacteistics fo measuement of 6-8

30 adiated emissions, they ae not ideal fo gatheing data ove a wide ange of fequencies. The adiated emissions ange typically extends fom 3 MHz to 6 GHz, and the length of a dipole must be physically adjusted to povide a length of ½ λ at each measuement fequency. A moe pactical technique is to employ boadband measuement antennas. A boadband antenna has the following chaacteistics:. The input/output impedance is faily constant ove the fequency band.. The antenna patten is faily constant ove the fequency band. Two types of boadband antennas will be examined: The biconical antenna, and the log-peiodic antenna. The biconical antenna is typically used in the fequency ange of 3 MHz to MHz. The log-peiodic antenna is typically used in the band fom MHz to GHz. Biconical Antennas An infinite biconical antenna consists of two cones of half angle h with a small gap at the feed point. z E fee space h H φ voltage souce h 6-9

31 f k g n the space suounding the cones J. Symmety suggests that the fields ae H φ h H φ and i E j E. Maxwell s equations can be solved to give the fom of the field as and E H φ H e sin jk jk k H e η H ωε sin φ hee H is constant. t is noted that these fields fom tansvese electomagnetic (TEM) waves (the electic and magnetic fields ae othogonal and tansvese to the diection of popagation). Theefoe, a unique voltage between two points on the cones may be defined. The voltage poduced between two points on opposite cones that ae both a distance fom the feed point is h k V ( ) E d l π η H e jk ln c ot h The cuent on the suface of the cones is given by π φ φ ( ) H sin dφ h πh e jk and the input impedance is then in V ( ) ( ) η ln co t h π which is puely esistive. ln cot h 6-3

32 i l Usually, the cone half-angle is chosen to povide a match to the feed line chaacteistic impedance. The total time aveage adiated powe is given by P d s s π π h φ h E sin d d φ η πη H h d sin πη H ln c ot n Radiation esistance is given by o R η ( ) R H ln c ot H ln cot h which is the same as the input impedance in. t is noted that the adiated fields ae spheical waves with E in the diection and H in the m diection. Fo linealy polaized waves incident on the antenna fom the boadside diection ( 9 o ), the antenna esponds to the field component that is paallel to its axis. Also the input impedance and patten ae theoetically constant ove an infinite ange of fequencies. nfinite length cones ae obviously impossible to constuct, theefoe eal biconical antennas consist of tuncated cones. The finite length of the cones causes eflections as the waves tavel outwad along the cones. This poduces standing waves that esult in the input impedance having an imaginay (eactive) component, athe than being puely eal. Often wies ae used to appoximate the cone sufaces: h 6-3

33 tuncated biconical antenna composed of wie elements Othe vaiations: cone gound plane Discone Bowtie The fields of the discone antenna above the gound plane ae the same as those of the biconical antenna by the method of images. The adiation esistance of the discone is ½ that of the biconical antenna. The bow-tie antenna consists of flat tiangula plates o a wie which outlines the same aea as the plates. The bow-tie antenna is fequently used fo eception of the UHF television signals. Using wies instead of solid metal tiangles tends to educe the bandwidth of the bow-tie antenna. Log-peiodic antennas The log-peiodic antenna achieves a lage opeational bandwidth though epetitive dimensioning of stuctues. The stuctual dimensions incease in popotion to the distance fom the oigin of the stuctue. As a esult, the input impedance and adiation popeties epeat peiodically and ae functions of the logaithm of fequency. The log-peiodic dipole aay is a common log-peiodic measuement antenna. This antenna shaes the popeties of all log-peiodic antennas in that element distances, lengths, and sepaations ae elated by a constant such that ln d n τ l d R R n n n n 6-3

34 α l n l l n n + R n d n log-peiodic aay The most efficient way of opeating a log-peiodic aay is such that the cuents on adjacent elements ae evesed in phase. ciss-coss feed method n this way the shote elements will not intefee with elements to the ight. The bandwidth of the log-peiodic antenna is appoximated by detemining the fequency at which the shotest element is, and the fequency at which the longest element is ½ λ. At a paticula fequency only the elements which ae at o nea a esonance ae active. Thus, the active egion of the antenna adjusts depending on fequency. 6-33

35 high fequency measuement low fequency measuement emitte emitte active egion active egion 6. Apetue antennas Apetue antennas ae chaacteized by an apetue o opening fom which adiated fields ae emitted. These include hons, slots and micostip patch antennas. The opeation of such antennas is best explained by Huygen s pinciple: Each point in an advancing wavefont acts as a souce of spheical, seconday wavelets, that popagate outwad. ncident field The seconday wavelets cause the wave to spead as it tavels away fom the apetue. 6-34

36 n p n n n This is known as diffaction. The antenna patten of an apetue antenna is actually a diffaction patten. n the fa zone of a simple apetue the magnitude of the electic field is given by jk e E ( ) E ( ) a π ( ) S jk d s whee S is the apetue suface, E a o is the magnitude of the electic field in the apetue and is a position vecto that sweeps ove points in the apetue. At points fa fom the apetue p z co s Assuming that the field in the apetue is unifom and that the apetue width is small (,, φ) E a / jk jk xe jk z co s E a e d z je a π a / e jk a sin π co s λ π co s The size of the main lobe in the esulting patten is invesely popotional to the apetue width a. Thus in ode fo the main lobes to be naow, the apetue dimensions must be on the ode of a wavelength o geate. z S x No m alized fa-zone E-field vs. Obsevation angle a ds z c o s E (nom alized) x. Radiation fom a naow apetue Theta (degees) Hon antennas 6-35

37 q Hon antennas ae flaed waveguides. Thee ae thee basic types of hon antennas. E-plane hon - flae is in the plane that contains the H-plane hon - flae is in the plane that contains the Pyamidal hon - flae is in both planes. oe -field vecto. H -field vecto. The apetue distibution of a hon is typically the same as the mode of the feeding waveguide, with a phase tape acoss the apetue. 3 E. 57λ z. 5λ Geomety of a typical hon antenna H The antenna as a eceiving element Any tansmitting antenna can also be used fo the pupose of eceiving intecepting a potion of the powe adiated by some souce. nstead of being diven by tansmission line, a eceiving antenna delives powe to a load connected at its teminals. Conside a spheical wave adiated by some distant souce, and incident on a eceiving antenna. Ove the local egion of the antenna, the spheical wave can be appoximated as a plane wave. The plane wave induces a cuent in the antenna, which in tun poduces an additional scatteed field. But the induced cuent also causes a voltage to appea acoss the load impedance. This voltage then acts like a diving voltage causing additional cuents to flow, just as in a tansmitting antenna, which poduce still anothe scatteed field. Thus, by supeposition, the total cuent flowing on the antenna may be viewed as that due to a scattee inteacting with a plane wave plus that of a tansmitting antenna. Tansmitting/eceiving equivalent cicuits 6-36

38 t V + V + netwok desciption of tansmitting/eceiving system Assume: << fo lage (little coupling fom eceiving to tansmitting antenna) V + ( ) in V + V - linea medium s E t antenna (tansmitting) L antenna (eceiving) + V - Equivalent cicuit fo tansmitting antenna V + L + L 6-37

39 u + - L Equivalent cicuit fo eceiving antenna Note: hen antenna is in eceiving, we can not assume since this tem descibes the coupling effect between tansmitte and eceive. Note: hen antenna is tansmitting, then so that V + ( ) in V ( ) in Receiving/tansmitting ecipocity Thee ae thee basic ecipocity elations between eceiving and tansmitting antennas: ) The antenna patten fo eception is identical to that fo tansmission. ) The equivalent impedance in the eceiving antenna equivalent cicuit is identical to the input impedance of the antenna when it is tansmitting. 3) The effective eceiving coss-section aea of an antenna is popotianal to its diective gain as a tansmitting element. e have aleady consideed () above. The othes equie the use of the Loentz ecipocity theoem. Fom this theoem we can show that Relationship between gain and effective eceiving coss-sectional aea A Definition: effective eceiving coss-section aea (m ). e P a v P a v whee: eceived powe (powe deliveed to the load) aveage Poynting vecto (powe density) maintained by tansmitting

40 A e is a function of: antenna (atts/m ) ) Load impedance ) Aspect of antenna to oncoming wave 3) Polaization of oncoming wave Note: A e Pav total powe intecepted by eceiving antenna. g d t, d Ω t ( φ ) Recall: diective gain of tansmitting antenna, tansmitted powe. dt t Pav Pav t t g dt A g e t dt So: eceived powe in tems of tansmitted powe. Maximum powe tansfe elation: Assume load impedance is conjugate matched maximum powe tansfeed to load + - L eceiving antenna L R jx R R R 8 R 6-39

41 + V - tansmitting antenna R + jx t R t 8 R R 4 R R but: so: R R A π R R A π e e g dt g dt t A g e dt 4 R R antenna tansmitting, antenna eceiving antenna eceiving, antenna tansmitting now use o (Recipocity of netwok) g A g A dt e dt e A g e dt A g 6-4 e dt

42 Now since antennas and wee abitay, A g e d t constant Fo polaization matched conditions (eceiving antenna oiented to intecept maximum amount of powe), the constant can be shown to be Thus, A g e d λ λ (Deivation is kind of messy). Univesal elationship between gain of an antenna acting as a tansmitte and effective aea of same antenna acting as a eceive. So, λ D D t t Fiis equation Recipocity between tansmission and eception pattens Case ) Antenna tansmitting, antenna eceiving (b) () (a) Measue tansmitting patten of antenna by vaying. t 4 R R 6-4

43 b a b a Case ) Antenna tansmitting, antenna eceiving (b) () (a) Measue eceiving patten of antenna by vaying. t 4 R R b a b a b b By ecipocity: powe pattens ae equal. Thus, the eception patten of an antenna is identical to its tansmission patten. a a Refeences. Demaast, K. Engineeing Electomagnetics, Pentice Hall nc., 998. Paul, C. ntoduction to Electomagnetic Compatibility, John iley & Sons,