Outline. Physical bounds on antennas of arbitrary shape. Physical bounds on antennas. Background

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Outline Phyil bound on ntenn of rbitrry hpe Mt Gutfon (Gerhrd Kritenon, Lr Jonon Mriu Cimu, Chritin Sohl) Deprtment of Eletril nd Informtion Tehnology Lund Univerity, Sweden Motivtion nd bkground

bet ntenn onfined to given (rbitrry) geometry, e.g., pheroid, ylinder, ellipti dik, nd retngle. Trdeoff between performne nd ize. Performne in Diretivity bndwidth produt: D/ (hlf-power B /).

964 Collin & Rothhild: Cloed form expreion of for rbitrry pheril mode, ee lo Hrrington, Collin, Fnte, Mlen, Gyi, Hnen, Hujnen, Sten, Thiele, Bet, Yghjin,... (mot re bed on Chu pproh uing pheril mode.

1 Outline Phyil bound on ntenn of rbitrry hpe Mt Gutfon (Gerhrd Kritenon, Lr Jonon Mriu Cimu, Chritin Sohl) Deprtment of Eletril nd Informtion Tehnology Lund Univerity, Sweden Motivtion nd bkground Antenn bound bed on forwrd ttering 3 Antenn bound nd optiml urrent bed on tored 4 Conluion Loughborough Antenn & Propgtion Conferene, --4 Phyil bound on ntenn Bkground ) z^ b) z^ ) Propertie of the bet ntenn onfined to given (rbitrry) geometry, e.g., pheroid, ylinder, ellipti dik, nd retngle. Trdeoff between performne nd ize. Performne in Diretivity bndwidth produt: D/ (hlf-power B /). Prtil relized gin: ( Γ )G over bndwidth. d) 947 Wheeler: Bound bed on iruit model. 948 Chu: Bound on nd D/ for phere. 964 Collin & Rothhild: Cloed form expreion of for rbitrry pheril mode, ee lo Hrrington, Collin, Fnte, Mlen, Gyi, Hnen, Hujnen, Sten, Thiele, Bet, Yghjin,... (mot re bed on Chu pproh uing pheril mode.) 999 Foltz & MLen, Sten, Koivito, nd Hujnen: Attempt for bound in pheroidl volume. 6 Thl: Bound on for mll hollow pheril ntenn. 7 Gutfon, Sohl, Kritenon: Bound on D/ for rbitrry geometrie (nd for mll ntenn). Yghjin & Sturt: Bound on for dipole ntenn in the limit k. ndenboh: Bound on for mll (non-mgneti) ntenn in the limit k. Chl, Sertel, nd olki: Bound on uing hrteriti mode. Gutfon, Cimu, Jonon: Optiml hrge nd urrent ditribution on ntenn.

2 Bkground: Chu bound (phere) Outline 5 5 Chu bound k Clultion of the tored nd rdited power outide phere with rdiu give the Chu-bound (948) for omni-diretionl ntenn, i.e., Chu = (k ) 3 + k nd D 3 Chu 3 (k ) 3 for k, where k = k i the reonne wvenumber k = π/λ = πf/. Motivtion nd bkground Antenn bound bed on forwrd ttering 3 Antenn bound nd optiml urrent bed on tored 4 Conluion New phyil bound on ntenn (7) Antenn identity (um rule) Lole linerly polrized ntenn Given geometry,, e.g., phere, retngle, pheroid, or ylinder. Determine how D/ (diretivity bndwidth produt) for optiml ntenn depend on ize nd hpe of the geometry. Solution: D ηk3 (ê γe ê + (ˆk ê) γ π m (ˆk ê) ) i bed on Antenn forwrd ttering Mthemtil identitie for Herglotz funtion M. Gutfon, C. Sohl, G. Kritenon: Phyil limittion on ntenn of rbitrry hpe Proeeding of the Royl Soiety A, 7 M. Gutfon, C. Sohl, G. Kritenon: Illutrtion of new phyil bound on linerly polrized ntenn IEEE Trn. Antenn Propgt. k^ ( Γ (k) )D(k; ˆk, ê) k 4 dk = η (ê γe ê+(ˆk ê) γ ) m (ˆk ê) ( Γ (k) )D(k; ˆk, ê): prtil relized gin, f., Frii trnmiion formul. Γ (k): refletion oeffiient D(k; ˆk, ê): diretivity k = π/λ = πf/ : wvenumber ˆk: diretion of rdition ê: polriztion of the eletri field, E = E ê. γ e : eletro-tti polrizbility dydi of the truture. γ m : mgneto-tti polrizbility dydi (ume γ m = ) η < : generlized (ll petrum) borption effiieny (η / for mll ntenn).

3 Cylindril dipole Cirumribing retngle Diretivity D/. mx D 7Ω D(k;x,z) ^ ^ z^ x^ D//(k ) 3 phyil bound Chu bound, k.5 (-j (k)j ) D(k;x,z) ^ ^ Lole ẑ-direted dipole, wire dimeter d = l/, mthed to 7 Ω. Weighted re under the blk urve (prtil relized gin) i known. Note, hlf wvelength dipole for k = π/.5 with diretivity D.64.5 db i. k d. = =/ /.. Note, η / for mll optiml ntenn k. Retngle, ylinder, ellipti dik, nd pheroid High-ontrt polrizbility dydi: γ. D//(k ) 3 Chu bound, k e r =/ r /... e γ i determined from the indued normlized urfe hrge denity, ρ, γ ê = rρ(r) ds where ρ tifie the integrl eqution ρ(r ) 4π r r ds = r ê + C n with the ontrint of zero totl hrge n ρ(r) ds= ) b) + % - equipotentil line + % - E E Cn lo ue FEM (Lple eqution). equipotentil line

4 Outline Bound bed on the tored Motivtion nd bkground Antenn bound bed on forwrd ttering 3 Antenn bound nd optiml urrent bed on tored Yghjin nd Sturt, Lower Bound on the of Eletrilly Smll Dipole Antenn, TAP. Bound on for mll dipole ntenn (in the limit k ). ndenboh, Simple proedure to derive lower bound for rdition of eletrilly mll devie of rbitrry topology, TAP. Bound on for mll (non-mgneti) ntenn (in the limit k ). Chl, Sertel, nd olki, Computtion of the Limit for Arbitrry-Shped Antenn Uing Chrteriti Mode, APS. Bound on not retrited to mll k. 4 Conluion Here, we reformulte the D/ bound n optimiztion problem tht i olved uing vrition pproh nd/or Lgrnge multiplier, ee Phyil Bound nd Optiml Current on Antenn, IEEE-TAP (in pre). Bound on D/ or D/ Chu derived bound on nd D/ for dipole ntenn. Mot pper nlyze for mll pheril dipole ntenn. Reult re independent of the diretion nd polriztion o D = 3/ nd it i uffiient to determine for thi e. The D/ reult re dvntgeou for generl hpe : they provide methodology to quntify the performne for different diretion nd polriztion. they n eprte liner nd irulr polriztion. D/(k 3 3 ) pper to depend reltively wekly on k in ontrt to k D//(k) 3 4 k x =3 k x = k x =f,.,g.. k x = k x = k x =3.. k x =. z/ z/ Diretivity in the rdition intenity P (ˆk, ê) nd totl rdited power P rd -ftor D(ˆk, ê) = 4π P (ˆk, ê) P rd = ωw P rd = kw P rd, where W = mx{w e, W m } denote the mximum of the tored eletri nd mgneti energie. The D/ quotient nel P rd D(ˆk, ê) = πp (ˆk, ê) J(r) n^ k^

5 D/ in the urrent denity J Smll ntenn k Rdition intenity P (ˆk, ê) P (ˆk, ê) = ζ k 3π Stored eletri w (e) = ê J(r)e jkˆk r d, W (e) v = 6πk w (e) J J o(kr ) k ( k J J R J J ) in(kr ) d J(r) n^ k^ Expnd for k D mx ρ,j () k3 mx { Eletri dipole J () = ê rρ(r) + ĥ r J () (r) d ρ ρ R D e k 3 mx e ρ 4π d d, J () () J ê rρ(r) d. ρ(r )ρ (r ) 4π r r d d R d d }, where J = J(r ), J = J(r ), R = r r. D(ˆk, ê) = k 3 ê J(r)e jkˆk r d mx{w (e) (J), w (m) (J)}, With the olution D e (ˆk, ê) e k3 4π ê γ ê. It verifie our previou bound.. D//(k) 3 ombined eletri mgneti z/... Non-eletrilly mll ntenn Strip dipole ξ = d/l = {.,.,.} Reformulte the D/ bound the minimiztion problem min J J o(kr ) J R k ( k J J J J ) in(kr ) d d, ubjet to the ontrint ê J(r)e jkˆk r d =. Solve uing Lgrnge multiplier. It give bound nd the optiml urrent ditribution J.... D//(k) 3 k x =3 k x = k x =f,.,g.. D/ bound for retngle. J x elf reonnt y loded J x /mx(j x ). o(¼x/ x).. Optiml urrent on trip. z/ x/ D//(k) k J x elf reonnt y loded The tr indite the performne of trip dipole with ξ =.. Almot no dependene on k for D/(k 3 3 ). More dependene on k for D nd k 3 3. Note the diretivity of the hlf-wve dipole, D.64. The optiml urrent ditribution i loe to o(πx/l). J /m x

6 Optiml urrent ditribution on mll phere Optiml urrent ditribution on mll phere The optimiztion problem for mll dipole ntenn how tht the hrge ditribution i the mot importnt quntity. On phere, we hve ρ(θ, φ) = ρ o θ for optiml ntenn with polriztion ê = ẑ. The urrent denity tifie J = jkρ Some olution: Spheril dipole, β =, A =. Cpped dipole, β =, A =. Folded pheril helix, β =, A. They ll hve lmot identil hrge ditribution ) b) J /J ± 45± 9± 35± 8± J /J ± ± ± ± Mny olution, e.g., ll urfe urrent J = J θˆθ( in θ β ) A + in θ in θ φ ˆθ A θ ˆφ where J θ = jkρ, β i ontnt, nd A = A(θ, φ) ρ(θ, φ) = ρ o θ Cn mthemtil olution ugget ntenn deign? ) J/J.5.5 Á 45± 9± 35± 8± Outline Conluion Motivtion nd bkground Antenn bound bed on forwrd ttering 3 Antenn bound nd optiml urrent bed on tored 4 Conluion Forwrd ttering nd/or optimiztion to determine bound on D/ for rbitrry hped ntenn. Cloed form olution for mll ntenn. Performne in the polrizbility of the ntenn truture. Forwrd ttering nd optimiztion pproh oinide for k. Lgrnge multiplier to olve the optimiztion problem for lrger truture. D/(k 3 3 ) nerly independent on k for < k <.5. Optiml urrent ditribution. ) b) ) ± 45± 9± 35± 8± J /J J /J J/J Á ± ± ± ± ± 9± 35± 8±

Experiment Study on the Interior Sound Field of Water Filled Pipe with Elastic Wall

Experiment Study on the Interior Sound Field of Water Filled Pipe with Elastic Wall Interntion Indutri Informti nd Computer Engineering Conferene (IIICEC 5 Experiment Stud on the Interior Sound Fied of Wter Fied Pipe with Eti W Lu Xueong,, Li Qi,b, Liu Jun, Aouti Siene nd Tehnoog Lbortor,